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Math Help - Double ntegral over the first quarter of a circle

  1. #1
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    Double ntegral over the first quarter of a circle

    Hello from Greece...

    Can someone help me solve this exercise please ???

    Compute the integral \int_{0}^{1}\int_{0}^{\sqrt{1-x^2}}(x^2+y^2)dydx in the first quarter of a circle with a radius of one

    thank you Merry Christmas, Happy Holidays !!!

    Last edited by mr fantastic; December 21st 2011 at 02:53 PM. Reason: Title.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Re: HELP with integral in the first quarter of a circle

    Quote Originally Posted by kotsos View Post
    Hello from Greece...

    Can someone help me solve this exercise please ???

    Compute the integral \int_{0}^{1}\int_{0}^{\sqrt{1-x^2}}(x^2+y^2)dydx in the first quarter of a circle with a radius of one

    thank you Merry Christmas, Happy Holidays !!!

    Start by evaluating the inner integral wrt y.
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: HELP with integral in the first quarter of a circle

    Another hint: using polar coordinates you'll obtain \int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho .
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    Re: HELP with integral in the first quarter of a circle

    Quote Originally Posted by FernandoRevilla View Post
    Another hint: using polar coordinates you'll obtain \int_0^{\pi/2}d\theta\int_{0}^1\rho^3\;d\rho .
    i found pi/8=0,3926....is it right ?
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Re: HELP with integral in the first quarter of a circle

    Quote Originally Posted by kotsos View Post
    i found pi/8=0,3926....is it right ?
    Right.
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  6. #6
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    Re: HELP with integral in the first quarter of a circle

    thank you SIR !!!
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