# [SOLVED] Help me to solve this math problems

• August 22nd 2009, 03:10 AM
wizard654zzz
[SOLVED] Help me to solve this math problems
Let : $x=\sin \theta$
Are you required to use integration by parts? The obvious way to integrate this is to let $y= 1- x^2$ so that $dy= -2x dx$ or $-\frac{1}{2}dy= x dx$, $x^2= 1- y$ and the integral becomes $\int \frac{(x^2)(x dx)}{\sqrt{1- x^2}}= -\frac{1}{2}\int\frac{(1- y)dy}{\sqrt{y}}$ $= -\frac{1}{2}\int\frac{(1- y)dy}{y^{\frac{1}{2}}}$ $= -\frac{1}{2}\int \left(y^{-\frac{1}{2}}- y^{\frac{1}{2}}\right)dy$.