# Integration problem

• November 9th 2009, 07:46 AM
Integration problem
Integrate sqrt(x - x^2)

I've been struggling with this question for hours but has come no closer to solving it. I know it involes the sin inverse function but I cant find a suitable substitution to make that happen.

Would appreciate any help
• November 9th 2009, 08:09 AM
galactus
As with most of these, there are various ways to go about it.

$\int\sqrt{x-x^{2}}dx$

$\int\sqrt{x(1-x)}dx$

Make the sub $x=\frac{2u+1}{2}, \;\ dx=du$

and we get $\frac{1}{2}\int\sqrt{1-4u^{2}}du$

Now, there are many routes to take, but a trig sub may be OK.

Can you do it from here?.
• November 9th 2009, 08:37 AM