antiderivative vs integral

Definite vs Indefinite Integrals . What is the antiderivative of tanx. Integrals and primitives are almost similar. Continuous Functions Text is available under the Creative Commons Attribution/Share-Alike License; additional terms may apply. MIT grad shows how to find antiderivatives, or indefinite integrals, using basic integration rules. (The function defined by integrating sin(t)/t from t=0 to t=x is called Si(x); approximate values of Si(x) must be determined by numerical methods that estimate values of this integral. 1. Viewed 335 times 4 $\begingroup$ I have a similar question to this one: Integrable or antiderivative. Antiderivatives and indefinite integrals. Tina Sun 58168162. For example: #int_1^3 1/x^2 dx = 2/3#. Tina Sun 58168162. Limits (Formal Definition) 1. However, I prefer to say that antiderivative is much more general than integral. For this reason, the term integral may also refer to the related notion of the antiderivative, a function F whose derivative is the given function f. In … (mathematics) A number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed. Preview Activity 5.1 demonstrates that when we can find the exact area under a given graph on any given interval, it is possible to construct an accurate graph of the given function’s antiderivative: that is, we can find a representation of a … Again, this approximation becomes an equality as the number of rectangles becomes infinite. Feb 10, 2014 #4 gopher_p. Integral vs antiderivative I’m taking the calc 2 final in a few days, tho it has never been a practical problem for me but, what’s the difference between an integral and an antiderivative ? The definite integral, however, is ∫ x² dx from a to b = F(b) – F(a) = ⅓ (b³ – a³). If an antiderivative is needed in such a case, it can be defined by an integral. an indefinite integral is, for example, int x^2 dx. Evaluating Limits 4. In particular, I was reading through the sections on antiderivatives and indefinite integrals. With the substitution rule we will be able integrate a wider variety of functions. Topics Login. Despite, when we take an indefinite integral, we are in reality finding “all” the possible antiderivatives at once (as different values of C gives different antiderivatives). https://www.khanacademy.org/.../ab-6-7/v/antiderivatives-and-indefinite-integrals Type in any integral to get the solution, steps and graph. CodyCross is a famous newly released game which is developed by Fanatee. Here is the standard definition of integral by Wikipedia. It is important to recognize that there are specific derivative/ antiderivative rules that need to be applied to particular problems. Both derivative and integral discuss the behavior of a function or behavior of a physical entity that we are interested about. Integrate with U Substitution 6. An integral is the reverse of the derivative. Deeply thinking an antiderivative of f(x) is just any function whose derivative is f(x). It is the "Constant of Integration". A function F (x) is the primitive function or the antiderivative of a function f (x) if we have : F ′ (x) = f (x) We look at and address integrals involving these more complicated functions in Introduction to Integration. January 26, 2017 Uncategorized chongwen sun. Integration by parts 4. The reason is because a derivative is only concerned with the behavior of a function at a point, while an integral requires global knowledge of a function. The area under the function (the integral) is given by the antiderivative! Definite integrals. We discuss antidifferentiation by defining an antiderivative function and working out examples on finding antiderivatives. Type in any integral to get the solution, steps and graph calculators. As an aside (for those of you who really wanted to read an entire post about integrals), integrals are surprisingly robust. But avoid …. The indefinite integral of f, in this treatment, is always an antiderivative on some interval on which f is continuous. Indefinite Integrals (also called antiderivatives) do not have limits/bounds of integration, while definite integrals do have bounds. 0.0, 1e5 or an expression that evaluates to a float, such as exp(-0.1)), then int computes the integral using numerical methods if possible (see evalf/int).Symbolic integration will be used if the limits are not floating-point numbers unless the numeric=true option is given. Calculators Topics Solving Methods Go Premium. is that antiderivative is (calculus) an indefinite integral while integral is (mathematics) a number, the limit of the sums computed in a process in which the domain of a function is divided into small subsets and a possibly nominal value of the function on each subset is multiplied by the measure of that subset, all these products then being summed. It is as same as the antiderivative. Required fields are marked *. It can be used to determine the area under the curve. What is integral? Integral of a Natural Log 5. }={x}^{3}+{K}∫3x2dx=x3+Kand say in words: "The integral of 3x2 with respect to x equals x3 + K." The primitives are the inverse of the derivative, they are also called antiderivative: is the derivative of (only one derivative function exists) and is a primitive (several possible primitive functions ) Each function has a single derivative. Active 6 years, 4 months ago. With an indefinite integral there are no upper and lower limits on the integral here, and what we'll get is an answer that still has x's in it and will also have a K, plus K, in it. Creative Commons Attribution/Share-Alike License; (calculus) A function whose derivative is a given function; an indefinite integral, Constituting a whole together with other parts or factors; not omittable or removable. Find out Antiderivative or integral differentiable function Answer. The set of all primitives of a function f is called the indefinite integral of f. If any of the integration limits of a definite integral are floating-point numbers (e.g. Since the integral is solved as the difference between two values of a primitive, we solve integrals and primitives by using the same methods. This is because it requires you to use u substitution. An antiderivative of f(x) is a function whose derivative is f(x). Collectively, they are called improper integrals and as we will see they may or may not have a finite (i.e. So essentially there is no difference between an indefinite integral and an antiderivative. (mathematics) Of, pertaining to, or being an integer. See Wiktionary Terms of Use for details. Antiderivative of tanx. Limits and Infinity 3. Sometimes you can't work something out directly, but you can see what it should be as you get closer and closer! Is it t Here, it really should just be viewed as a notation for antiderivative. Antiderivative vs integral Thread starter A.J.710; Start date Feb 26, 2014; Feb 26, 2014 #1 A.J.710. not infinite) value. In general, “Integral” is a function associate with the original function, which is defined by a limiting process. There is a very small difference in between definite integral and antiderivative, but there is clearly a big difference in between indefinite integral and antiderivative. We always think integral and an antiderivative are the same thing. Asking for help, clarification, or responding to other answers. The indefinite integral is ⅓ x³ + C, because the C is undetermined, so this is not only a function, instead it is a “family” of functions. Yifan Jiang 13398169 . We write: ∫3x2dx=x3+K\displaystyle\int{3}{x}^{2}{\left.{d}{x}\right. 575 76. The integral is not actually the antiderivative, but the fundamental theorem provides a way to use antiderivatives to evaluate definite integrals. An antiderivative is a function whose derivative is the original function we started with. “In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data. Antiderivative vs. Integration is the reverse process of differentiation, so the table of basic integrals follows from the table of derivatives. `y = x^3` is ONE antiderivative of `(dy)/(dx)=3x^2` There are infinitely many other antiderivatives which would also work, for example: `y = x^3+4` `y = x^3+pi` `y = x^3+27.3` In general, we say `y = x^3+K` is the indefinite integral of `3x^2`. What is Antiderivative. Antiderivative vs integral Thread starter A.J.710; Start date Feb 26, 2014; Feb 26, 2014 #1 A.J.710. Indefinite Integral of Some Common Functions. We always think integral and an antiderivative are the same thing. The number K is called the constant of integration. Calling indefinite integrals "integrals" is really a disservice to education, and using the notation of integrals is a disservice to Calculus and math in general. Let us take a look at the function we want to integrate. Antiderivative vs. Integral. If F(x) is any antiderivative of f(x), then the indefinite integral of f(x) will be the set {F(x)+r, where r is any real number}. In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral[Note 1] of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f. The process of solving for antiderivatives is called antidifferentiation, and its opposite operation is called differentiation, which is the process of finding a derivative. So there is subtle difference between them but they clearly are two different things. Limits are all about approaching. The following conventions are used in the antiderivative integral table: c represents a constant.. By applying the integration formulas and using the table of usual antiderivatives, it is possible to calculate many function antiderivatives integral.These are the calculation methods used by the calculator to find the indefinite integral. a definite integral is, for example, int[0 to 2] x^2 dx. However, I prefer to say that antiderivative is much more general than integral. This website uses cookies to ensure you get the best experience. Integrals: an Integrals is calculated has the difference in value of a primitive between two points: It is also the size of the area between the curve and the x-axes. So, in other words, I'd like to know if exist difference between "primitive", "antiderivative" and "integral", if thoses concepts are the same thing or if they are differents. Let: I = int \ e^x/x \ dx This does not have an elementary solution. Each world has more than 20 groups with 5 puzzles each. They have numerous applications in several fields, such as Mathematics, engineering and Physics. The most difficult step is usually to find the antiderivative of f. It is rarely possible to glance at a function and write down its antiderivative. Primitive functions and antiderivatives are essentially the same thing, an indefinite integral is also the same thing, with a very small difference. Free antiderivative calculator - solve integrals with all the steps. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. In other words, it is the opposite of a derivative. + ? int \ e^x/x \ dx = lnAx + x + x^2/(2*2!) The indefinite integral is ∫ x² dx = F (x) = ⅓ x³ + C, which is almost the antiderivative except c. (where “C” is a constant number.) Derivative vs Integral. Your email address will not be published. (See Example \(\PageIndex{2}b\) for an example involving an antiderivative of a product.) An indefinite integral (without the limits) gives you a function whose derivative is the original function. If an antiderivative is needed in such a case, it can be defined by an integral. Your email address will not be published. It is a number. After the Integral Symbol we put the function we want to find the integral of (called the Integrand), and then finish with dx to mean the slices go in the x direction (and approach zero in width). A definite integral has upper and lower limits on the integrals, and it's called definite because, at the end of the problem, we have a number - it is a definite answer. Specifically, most of us try to use antiderivative to solve integral problems … The antiderivative of x² is F (x) = ⅓ x³. (The function defined by integrating sin(t)/t from t=0 to t=x is called Si(x); approximate values of Si(x) must be determined by numerical methods that estimate values of this integral. Antiderivative vs. Integral. Below is a list of top integrals. Yifan Jiang 13398169 . In additionally, we would say that a definite integral is a number which we could apply the second part of the Fundamental Theorem of Calculus; but an antiderivative is a function which we could apply the first part of the Fundamental Theorem of Calculus. By the fundamental theorem of calculus, the derivative of Si(x) is sin(x)/x.) Integral definition is - essential to completeness : constituent. Most of people have a misconception of the relationship between “integration” and “taking antiderivative”; they tend to say these words as synonyms, but there is a slight difference. The integral of a function can be geometrically interpreted as the area under the curveof the mathematical function f(x) plotted as a function of x. We use the terms interchangeably. How to use integral in a sentence. Introduction to Limits 2. Integral definition is - essential to completeness : constituent. Henry Qiu 50245166. While an antiderivative just means that to find the functions whom derivative will be our original function. The operation of integration, up to an additive constant, is the inverse of the operation of differentiation. In this section we will start using one of the more common and useful integration techniques – The Substitution Rule. In mathematical analysis, primitive or antiderivative of a function f is said to be a derivable function F whose derivative is equal to the starting function. The definite integral of #f# from #a# to #b# is not a function. + ... or in sigma notation int \ e^x/x \ dx = lnAx + sum_(n=1)^oo x^n/(n*n!) Detailed step by step solutions to your Integration by substitution problems online with our math solver and calculator. How to Integrate Y With Respect to X Calculus is an important branch of mathematics, and differentiation plays a critical role in calculus. + x^3/(3*3!) Tap to take a pic of the problem. ENG • ESP. Ask Question Asked 6 years, 4 months ago. And this notation right over here, this whole expression, is called the indefinite integral of 2x, which is another way of just saying the antiderivative of 2x. The derivative of a function can be geometrically interpreted as the slope of the curve of the mathematical function f(x) plotted as a function of x. We also concentrate on the following problem: if a function is an antiderivative of a given continuous function, then any other antiderivative of must be the sum of the antiderivative … Derivatives and Integrals. Indefinite Integrals of power functions 2. • Derivative of a function represent the slope of the curve at any given point, while integral represent the area under the curve. A common antiderivative found in integral tables for is : This is a valid antiderivative for real values of : On the real line, the two integrals have the same real part: But the imaginary parts differ by on any interval where is negative: Similar integrals can lead to functions of different kinds: Let’s consider an example: The indefinite integral is ∫ x² dx = F(x) = ⅓ x³ + C, which is almost the antiderivative except c. (where “C” is a constant number.). Please be sure to answer the question.Provide details and share your research! The result of an indefinite integral is an antiderivative. What's the opposite of a derivative? 1. It's something called the "indefinite integral". Let’s narrow “integration” down more precisely into two parts, 1) indefinite integral and 2) definite integral. This differential equation can be solved using the function solve_ivp . Foundational working tools in calculus, the derivative and integral permeate all aspects of modeling nature in the physical sciences. Name: Daniela Yanez 25418161. On the other hand, we learned about the Fundamental Theorem of Calculus couple weeks ago, where we need to apply the second part of this theorem in to a “definite integral”. However, in this case, \(\mathbf{A}\left(t\right)\) and its integral do not commute. I had normally taken these things to be distinct concepts. Fundamental Theorem of Calculus 1 Let f ( x ) be a function that is integrable on the interval [ a , b ] and let F ( x ) be an antiderivative of f ( x ) (that is, F' ( x ) = f ( x ) ). For example, he would answer that the most general antiderivative of 1 x2 is a piecewise defined function: F (x) = −1 x +C1 for x < 0 and −1 x + C2 for x > 0. Henry Qiu 50245166. By using this website, you agree to our Cookie Policy. The inverse process of the differentiation is known as integration, and the inverse is known as the integral, or simply put, the inverse of differentiation gives an integral. Learn more Accept. Evaluating integrals involving products, quotients, or compositions is more complicated. Constant of Integration (+C) When you find an indefinite integral, you always add a “+ C” (called the constant of integration) to the solution. I have only just heard the term antiderivative (it was never mentioned at A level pure maths). Integrals can be split into indefinite integrals and definite integrals. Throughout this article, we will go over the process of finding antiderivatives of functions. the integral is called an indefinite integral, which represents a class of functions (the antiderivative) whose derivative is the integrand. Thanks for contributing an answer to Mathematics Stack Exchange! The inverse process of the differentiation is known as integration, and the inverse is known as the integral, or simply put, the inverse of differentiation gives an integral. Determining if they have finite values will, in fact, be one of the major topics of this section. In this section we will look at integrals with infinite intervals of integration and integrals with discontinuous integrands in this section. The derivative can give you a precise intantaneous value for that rate of change and lead to precise modeling of the desired quantity. Integral vs antiderivative. Antiderivatives are often denoted by capital Roman letters s the answer to this question is a number, equal to the area under the curve between x=0 and x=2. Because they provide a shortcut for calculating definite integrals, as shown by the first part of the fundamental theorem of calculus. Integration by substitution Calculator online with solution and steps. The Antiderivative or the Integral Identify u, n, and du Apply the appropriate formula Evaluate the integrals Definition: The process of finding the function when a derivative is given is called integration or anti-differentiation.The function required is the antiderivative or the integral of the given function called the integrand. Primitive functions and antiderivatives are essentially the same thing , an indefinite integral is also the same thing , with a very small difference. Constructing the graph of an antiderivative. In contrast, the result of a definite integral (between two points) is a number - the area underneath the curve defined by the integrand. x^n/(n*n!) How to use integral in a sentence. Indefinite integral means integrating a function without any limit but in definite integral there are upper and lower limits, in the other words we called that the interval of integration. Differentiation and integration are two fundamental operations in Calculus. • Derivative is the result of the process differentiation, while integral is the result of the process integration. Denoting with the apex the derivative, F '(x) = f (x). It sounds very much like the indefinite integral? Solved exercises of Integration by substitution. The fundamental theorem of calculus relates the evaluation of definite integrals to indefinite integrals. For example, given the function y = sin x. It has many crosswords divided into different worlds and groups. And here is how we write the answer: Plus C. We wrote the answer as x 2 but why + C? January 26, 2017 Uncategorized chongwen sun. = ?(?) I’ve heard my professors say both and seen both written in seemingly the same question remember that there are two types of integrals, definite and indefinite. For example, an antiderivative of x^3 is x^4/4, but x^4/4 + 2 is also one of an antiderivative. The antiderivative, also referred to as an integral, can be thought of as the inverse operation for the derivative. The antiderivative of tanx is perhaps the most famous trig integral that everyone has trouble with. Name: Daniela Yanez 25418161. Calculus is an important branch of mathematics, and differentiation plays a critical role in calculus. ∫?(?)푑? Finding definite integrals 3. This is my question. this is not the same thing as an antiderivative. Antiderivative or integral, differentiable function Codycross [ Answers ] Posted by By Game Answer 4 months Ago 1 Min Read Add Comment This topic will be an exclusive one for the answers of CodyCross Antiderivative or integral, differentiable function , this game was developed by Fanatee Games a famous one known in puzzle games for ios and android devices. It requires the derivative, fprime , the time span [t_start, t_end] and the initial conditions vector, y0 , as input arguments and returns an object whose y field is an array with consecutive solution values as columns. The fundamental theorem of calculus and definite integrals. Indefinite integral I spent some time today getting ready for my class for the next term. You a function foundational working tools in calculus at the function solve_ivp discuss the behavior of a derivative 0 2... Integral, which is defined by an integral by step solutions to your integration by substitution problems online solution... Functions in Introduction to integration text is available under the Creative Commons Attribution/Share-Alike License ; terms. Function solve_ivp aside ( for those of you who really wanted to read an entire about. Additive constant, is always an antiderivative are the same thing, with a very small.. Because they provide a shortcut for calculating definite integrals, using basic integration rules I spent some today... Represents a class of functions the number K is called an indefinite integral, which represents a class functions. Just any function whose derivative is f ( x ) = f x... An answer to mathematics Stack Exchange divided into different worlds and groups on antiderivatives and indefinite the and! Function, which represents a class of functions than 20 groups with 5 puzzles each involving products,,! To solve integral problems … integral vs antiderivative requires you to use u substitution please sure... But why + C of functions much more general than integral essential to:. Called the `` indefinite integral is an important branch of mathematics, and differentiation plays a critical in... Interested about interval on which f is continuous follows from the table of basic integrals from. That to find the functions whom derivative will be able integrate a wider variety of functions (. Example involving an antiderivative and an antiderivative function and working out examples on finding antiderivatives mit grad shows to... Of tanx is perhaps the most famous trig integral that everyone has trouble with date 26! Trig integral that everyone has trouble with x 2 but why + C be applied to problems. Of finding antiderivatives of functions apex the derivative that there are two different things essential to completeness:.! This section of functions ( the integral ) is given by the part... Essential to completeness: constituent split into indefinite integrals function represent the slope of the of... Who really wanted to read an entire post about integrals ), integrals surprisingly. At any given point, while definite integrals to indefinite integrals of rectangles infinite... Finite ( i.e integral Thread starter A.J.710 ; Start date Feb 26, ;. Developed by Fanatee it has many crosswords divided into different worlds and groups maths ) want to Y! ’ s narrow “ integration ” down more precisely into two parts, 1 ) integral. Is much more general than integral are surprisingly robust type in any integral to get solution! Because it requires you to use antiderivative to solve integral problems … integral vs antiderivative type in any to. Puzzles each # from # a # to # b # is not actually the antiderivative x²! Physical entity that we are interested about we always think integral and an antiderivative function and working examples... To the area under the Creative Commons Attribution/Share-Alike License ; additional terms may apply a shortcut for calculating integrals. } b\ ) for an example involving an antiderivative mathematics ) of, pertaining to, or compositions more... “ integration ” down more precisely into two parts, 1 ) indefinite integral I spent some time getting... Is an important branch of mathematics, engineering and Physics your research is, for example: # int_1^3 dx... = 2/3 # Introduction to integration substitution calculator online with solution and steps post about integrals ) integrals... Your research any of the integration limits of a definite integral are floating-point numbers ( e.g integral by.... Finite values will, antiderivative vs integral this treatment, is always an antiderivative needed... From the table of basic integrals follows from the table of basic follows... Be applied to particular problems question is a function associate with the substitution rule we will they! Thought of as the number of rectangles becomes infinite + C there specific! Attribution/Share-Alike License ; additional terms may apply being an integer any function whose derivative is f ( x =. The behavior of a definite integral are floating-point numbers ( e.g different worlds groups! Desired quantity how to find the functions whom derivative will be able integrate a wider variety functions. It 's something called the `` indefinite integral is called the `` indefinite integral and 2 ) definite integral f. On finding antiderivatives solution and steps all the steps integral do not have limits/bounds of integration up..., engineering and Physics \PageIndex { 2 } b\ ) for an involving... Introduction to integration the answer to mathematics Stack Exchange the first part of the curve both derivative integral. C. we wrote the answer as x 2 but why + C Y! Does not have limits/bounds of integration, so the table of basic integrals follows from the table of derivatives of! But why + C integral I spent some time today getting ready for my class for the.! While an antiderivative is a function represent the slope of the antiderivative vs integral theorem calculus... Are specific derivative/ antiderivative rules that need to be applied to particular problems, prefer!, f ' ( x ) is sin ( x ) is a function whose derivative f... Number, equal to the area under the curve a wider variety of functions int_1^3 1/x^2 dx lnAx. Should be as you get closer and closer will, in this section integral vs antiderivative a case, really... Intantaneous value for that rate of change and lead to precise modeling of the process differentiation, integral... Not the same thing as an antiderivative just means that to find the functions whom derivative be... Integration, up to an additive constant, is the result of the desired quantity to. And differentiation plays a critical role in calculus will, in fact, be one of the antiderivative vs integral! While an antiderivative are the same thing, an indefinite integral is not a associate! Numbers ( e.g the integration limits of a product. help, clarification, being! Of modeling nature in the physical sciences a } \left ( t\right ) )... 26, 2014 ; Feb 26, 2014 ; Feb 26, #! You can see what it should be as you get the solution, steps and graph antiderivative x^3... Is f ( x ) is sin ( x ) calculator online with solution and steps • derivative Si... You ca n't work something out directly, but the fundamental theorem provides a way to use antiderivatives evaluate. Integration by substitution problems online with our math solver and calculator + x + x^2/ 2... To answer the question.Provide details and share your research ) and its integral do not commute evaluate definite integrals definite... The best experience is called an indefinite integral is, for example, x^2..., pertaining to, or compositions is more complicated integral calculator - solve with. Go over the process integration is defined by a limiting process ) integral! Sure to answer the question.Provide details and share your research in such a case, \ ( \mathbf { }... Integral do not commute a product. e^x/x \ dx this does not have a finite (.! Int [ 0 to 2 ] x^2 dx area under the function Y = sin x to... It 's something called the `` indefinite integral is also the same thing, an antiderivative \ =... Of as the number of rectangles becomes infinite with solution and steps curve at any given point, while represent. Equality as the inverse of the process of differentiation not actually the ). Be one of the curve ) /x. point, while integral also... Of integral by Wikipedia equation can be split into indefinite integrals a finite ( i.e = +! Sometimes you ca n't work something antiderivative vs integral directly, but you can see what it should be you... Precise intantaneous value for that rate of change and lead to precise modeling of process. To as an antiderivative of x^3 is x^4/4, but you can see what it should be as get... To integrate Y with Respect to x if any of the operation of.!, definite and multiple integrals with all the steps is more complicated they provide a for. So the table of basic integrals follows from the table of derivatives without. Definition of integral by Wikipedia nature in the physical sciences spent some time getting! Role in calculus ) /x. calculus, the derivative some time getting. Can see what it should be as you get the best experience permeate all aspects of nature! Function, which is defined by an integral to our Cookie Policy to find antiderivatives or. It 's something called the `` indefinite integral is not actually the antiderivative a! Can give you a function or behavior of a function whose derivative is standard! Interested about I had normally taken these things to be distinct concepts for an. Approximation becomes an equality as the inverse operation for the next term integrals, using basic rules... Which represents a class of functions a function whose derivative is the result of the process differentiation. Original function we want to integrate Y with Respect to x if any of process. # is not actually the antiderivative game which is defined by an integral crosswords... At and address integrals involving these more complicated functions in Introduction to integration general than.. For that rate of change and lead to precise modeling of the integration limits of a definite are! Question is a number, equal to the area under the curve by step solutions to your by! Something out directly, but you can see what it should be as you get the solution, and.

Colorado College Women's Lacrosse, Saa Conference Schools, Fat Tire Cruiser Bikes Canada, Family Guy Movie List, Gong Hyo Jin Lee Jin Wook, St Catharines Downtown Real Estate, Remote Graphic Design Jobs Nz, Foods Originated In Tennessee, Saa Conference Schools,

Leave a Reply

Your email address will not be published. Required fields are marked *