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Math Help - Double Integral with Polar Coordinates

  1. #1
    Member Em Yeu Anh's Avatar
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    Red face Double Integral with Polar Coordinates

    \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx
    Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.
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  2. #2
    Junior Member slovakiamaths's Avatar
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    Quote Originally Posted by Em Yeu Anh View Post
    \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx
    Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.
    put x=rcost and y=rsint, dxdy=rdrdt the solve it
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  3. #3
    Super Member 11rdc11's Avatar
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    Quote Originally Posted by Em Yeu Anh View Post
    \int_0^2\int_0^{\sqrt{2x-x^2}}5\sqrt{x^2+y^2}dydx
    Question asks to evaluate this by converting it into polar coordinates, I'm quite lost on this one.

    y = \sqrt{2x - x^2}

    y^2 = 2x -x^2

    y^2 + x^2 = 2x

    r^2 = 2r\cos{\theta}

    r = 2\cos{\theta}

    \int^{\frac{\pi}{2}}_{0} \int^{2\cos{\theta}}_{0} (5r)r drd\theta
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