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Q. 15

Expert-verified

Calculus

Found in: Page 260

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Explain the difference between two antiderivatives of the function.

The two functions are antiderivatives of each other if their difference is constant.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step1. Given

The two given functions are $f (x) and g (x)$ .

Step 2. Explanation

$Any two functions have the same derivative must differ by a constant . Algebraically, this means that to find one antiderivative of a function, then all other antiderivatives of that function differ from the one that find by a constant . Explanation The given functions g (x) and h (x) are both antiderivatives of some function f (x) . Rewrite the functions as, g' (x) = f (x) a n d h' (x) = f (x) . The difference of these functions is, g' (x) - h' (x) = 0 T his is by the difference rule means that, (8 (x) - h (x)) = 0 Use the result, " If is zero in the interior of / then is constant on / . Form the resul t, if g' (x) - (x) is zero then g (x) - h (x) i s c o n s \tan t . Therefore, g (x) - h (x) = C for some real number C .$

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