# Integrate sqrt(x-x^2)

by autodidude
Tags: integrate, sqrtxx2
 P: 333 1. The problem statement, all variables and given/known data Integrate $$\sqrt{x-x^2}$$ The attempt I did a trig substitution, letting $$cos(\theta)=\frac{x}{sqrt(x)}$$ and after some manipulation ended up with $$-2\int \ |sin(\theta)cos(\theta)|sin(\theta)cos(\theta) d\theta$$ which I have no idea how to integrate. If I make a u-substitution and let u=cos(theta) rather than simplify to get the above, I get $$2\int \ u\sqrt{u^2-u^4}du$$ which I cant make any progress on either.
Homework
 Quote by autodidude $$-2\int \ |sin(\theta)cos(\theta)|sin(\theta)cos(\theta) d\theta$$
 P: 584 Like Dick said. Look at it like this try to reformulate it so you get something like this: $$\int\sqrt{\frac{1}{4}-(x-}\frac{1}{2})^{2}dx$$ and substitute u : $$u=x-\frac{1}{2};dx=du$$ and see what you can get.