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Solution: Integrating Inverses of FunctionsIntegration by
Chapter 8, Problem 74E(choose chapter or problem)
Problem 74E
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 74E
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 3
Here, we have to evaluate the given integral.
.
We know that .
Therefore, we write the given equation as .