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Math Help - integral

  1. #1
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    integral

    Hi
    I wondered whats the best way to integrate \int x^2 \sqrt(1-x^2)

    Tried to substitute with u=1-x^2 That way i get x^2 = 1- u but I don't know how to continuoe.

    Thanks, knut
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  2. #2
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    e^(i*pi)'s Avatar
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    Re: integral

    Try x=\sin(u)
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  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: integral

    Quote Originally Posted by Knut-o View Post
    Hi
    I wondered whats the best way to integrate \int x^2 \sqrt(1-x^2)

    Tried to substitute with u=1-x^2 That way i get x^2 = 1- u but I don't know how to continuoe.

    Thanks, knut
    Where to dx gone?
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  4. #4
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    Re: integral

    Quote Originally Posted by Also sprach Zarathustra View Post
    Where to dx gone?
    \int x^2 \sqrt{1-x^2} dx
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  5. #5
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    Re: integral

    Quote Originally Posted by Knut-o View Post
    \int x^2 \sqrt{1-x^2} dx
    If you use the sub I made in my post then dx = \cos(u) \ du and your integral is \displaystyle \int \sin^2(u)\sqrt{1-\sin^2(u)} \cos(u) du = \int \sin^2(u)\cos^2(u) du

    Does that help?
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  6. #6
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    Re: integral

    yes! thank you very much
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