Antiderivative Of Square Root Of 2x

Antiderivative Of Square Root Of 2x Learn to define what antiderivatives are Discover how to find the antiderivative of constants and power functions See antiderivative rules and

There are 2 potential questions here One is the question of why the definite Riemann integral gives the correct notion of area under a curve for a nonnegative Riemann This means that the antiderivative x y x y cannot be a polynomial or rational function since such functions are changed when you differentiate them So y x 1 x y x 1 x is then a

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Antiderivative Of Square Root Of 2x
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66 I was wondering what the antiderivative of e x2 was and when I wolfram alpha d it I got e x2dx 1 2 erf x C So I of course didn t know what this erf was and I looked it up on This means that xxdx x x d x has no elementary antiderivative The specific reason to take Q x log x g Q x log x g as our differential field is that it is a field of trascendental elementary

Of course you can present it as f x x2 f x x 2 and apply the new integration by parts based on the quotient rule but I almost sure that a lot of the readers will rather think of the fact that 1 x2 As we know a non continuous function may have an antiderivative Thus the function may not be integrable That is although there is an explicitly defined antiderivative F x possibly not but

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Summarizing if f exp g has an elementary antiderivative with f and g rational functions g nonzero then it is of the form h exp g with h rational We work out particular examples of If so I think I get what you want to say If a antiderivative f exists such that f z 1 z the value of the two integrals should be equal Does that have anything to do with the fact that Ln z isn t

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Finding Antiderivatives Rules amp Examples Study

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Learn to define what antiderivatives are Discover how to find the antiderivative of constants and power functions See antiderivative rules and

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Calculus Why Is The Area Under A Curve The Integral

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There are 2 potential questions here One is the question of why the definite Riemann integral gives the correct notion of area under a curve for a nonnegative Riemann

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