Assume that f has an inverse on its domain. a. Let y = f -1 (x) and

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Assume that f has an inverse on its domain.

a. Let y = f-1(x) and show that yf'(y) dy. f

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.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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