# Integration by Parts - definite integral

• Sep 2nd 2008, 07:42 PM
symstar
Integration by Parts - definite integral
Just evaluate the integral...
$\int_{0}^{1/2}\sin^{-1}{x} dx$

I used...
$u=\sin^{-1}{x}$
$du=\frac{dx}{\sqrt {1-x^2}}$
$dv=dx$
$v=x$

The problem is that I get stuck with $\int_{0}^{1/2}\frac{xdx}{\sqrt {1-x^2}}$ eventually and I'm not quite sure where to go with it. I thought of maybe doing a sub, but I'm not sure what to sub for.
• Sep 2nd 2008, 07:46 PM
Chop Suey
Substitute $u = 1-x^2$.
• Sep 2nd 2008, 08:17 PM
symstar
Subbing $t=1-x^2$

$\frac{1}{2} \sin^{-1}{\frac{1}{2}} + \int_{3/4}^{1} \frac{dt}{-2\sqrt{t}}$

Is this correct so far?