# substitution problem

• Dec 11th 2009, 03:16 PM
Em Yeu Anh
substitution problem
If f is continuous on [0, $\pi$], use the substitution $u = \pi - x$ to prove that:

$\int_0^{\pi}xf(sinx)dx = \frac{\pi}{2}\int_0^{\pi}f(sinx)dx$

Completely lost here. $du = -1dx$ and I don't know how to start from there.
• Dec 11th 2009, 03:31 PM
Scott H
From

\begin{aligned}
u&=\pi-x\\
du&=-dx
\end{aligned}

we may derive

\begin{aligned}
x&=\pi-u\\
dx&=-du.
\end{aligned}

Hope this helps! :)