Let f : I → J be a bijective differentiable function froman interval I to an interval J, and let F : I → R be an anti-derivative of f. Find an explicit expression, in terms of f, f-1 and F, for an anti-derivative of f-1: J → I. [Both substitution and integration by parts may come in handy.]

Let f : I → J be a bijective differentiable function froman interval I to an interval J, and let F : I → R be an anti-derivative of f. Find an explicit expression, in terms of f, f-1 and F, for an anti-derivative of f-1: J → I. [Both substitution and integration by parts may come in handy.]

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.CR: Chapter 3 Review

Problem 12CR: Determine whether each of the following statements is true or false and explain why. The derivative...

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Question

Let f : I → J be a bijective differentiable function froman interval I to an interval J, and let F : I → R be an anti-derivative of f. Find an explicit expression, in terms of f, f^-1 and F, for an anti-derivative of f^-1: J → I. [Both substitution and integration by parts may come in handy.]

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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