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Q. 15

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.

See the step by step solution

Step by Step Solution

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.ExplanationThe given functions g(x) and h(x) are both antiderivatives of some function f(x). Rewrite the functions as, g'(x)=f(x) and h'(x) = f(x). The difference of these functions is, g'(x)-h'(x)=0 This 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 result, if g'(x)-(x) is zero then g(x)-h(x)is constant. Therefore, g(x)-h(x)=C for some real number C.


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