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

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- Nov 9th 2009, 08:46 AMadamantineIntegration 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 - Nov 9th 2009, 09:09 AMgalactus
As with most of these, there are various ways to go about it.

Make the sub

and we get

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

Can you do it from here?. - Nov 9th 2009, 09:37 AMadamantine
Can I use the trig sub of u = 1/2 sin p?