Okay, so here is the problem I have, which I am getting tripped up on for some reason:(adsbygoogle = window.adsbygoogle || []).push({});

a) Use integration by parts to show that

[tex]\int_{a}^{b} f(x) dx = bf(b) - af(a) - \int_{a}^{b} xf'(x) dx[/tex]

this was pretty easy, just regular old integration by parts with limits of integration.

b) Use the result in part (a) to show that if y = f(x) then

[tex] \int_{a}^{b} f(x) dx = bf(b) - af(a) - \int_{f(a)}^{f(b)} f^{-1}(y) dy[/tex]

I know that the inverse function of f(x) will leave me with x, which gets me to

[tex] \int_{a}^{b} f(x) dx = bf(b) - af(a) - \int_{a}^{b} f^{-1}(y) f'(x)[/tex]

but then what happens with f'(x)? For some reason I'm just totally spacing this out.

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# Homework Help: Integration By Parts

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