Integration by Substitution Problem

[theschaef]

Use the substitution u = pi - x to prove that

Integral {0 to pi} x * f(sinx) dx = (pi/2) Integral {0 to pi} f(sinx) dx

Not really sure what to do with this, so any help would be great. Thanks.

 

[galactus]

There's a nice proof here. Pages 3 and 4

http://www.math.ou.edu/~nbrady/teaching ... 23/am1.pdf