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Math Help - Integration problem

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