Integration by parts leads to a rule for integrating inverses that usually gives good results: The idea
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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 case ƒ -1(x), 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.
Transcribed Image Text:
[1¹(x) dx = [yf'(y) dy f(y) ) dy = yf(y) - [ƒ6). = xf '(x) - [ f(1) dy y = f(x), x = f(y) dx = f'(y) dy Integration by parts with u = y, du = f'(y) dy
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Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
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