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Solved: Integrating Inverses of FunctionsIntegration by
Chapter 8, Problem 71E(choose chapter or problem)
Problem 71E
Integrating Inverses of Functions
Integration by parts leads to a rule for integrating inverses that usually gives good results:
The idea is to take the most complicated part of the integral, in this f-1(x) case and simplify it first. For the integral of ln x, we get
For the integral of cos-1 x we get
Use the formula
to evaluate the integrals. Express your answers in terms of x.
Questions & Answers
QUESTION:
Problem 71E
Integrating Inverses of Functions
Integration by parts leads to a rule for integrating inverses that usually gives good results:
The idea is to take the most complicated part of the integral, in this f-1(x) case and simplify it first. For the integral of ln x, we get
For the integral of cos-1 x we get
Use the formula
to evaluate the integrals. Express your answers in terms of x.
ANSWER:
Solution
Step 1 of 2
In this problem, we need to evaluate the given indefinite integral using the given formula
Given formula
Where