# Math Help - Integration problem

1. ## 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

2. 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?.

3. Can I use the trig sub of u = 1/2 sin p?