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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integration By Parts

**Physics Forums | Science Articles, Homework Help, Discussion**