Assume that f has an inverse on its domain.

a. Let y = f^-1(x) and show that 

b. Use part (a) to show that

∫ f^-1(x) dx = y f(y) - ∫ f(y) dy.

c. Use the result of part (b) to evaluate ∫ ln x dx (express the result in terms of x).

d. Use the result of part (b) to evaluate ∫ sin^-1 x dx.

e. Use the result of part (b) to evaluate ∫ tan^-1 x dx.

Transcribed Image Text:

yf'(y) dy. f"(x) dx