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Math Help - Surface Integral help

  1. #1
    Junior Member
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    Surface Integral help

    Hey, really stuck on this question.

    Integrate

    f(x,y,z)= \sqrt{3x^2+3y^2+z+1}

    over the surface given by the graph z=g(x,y)=x^2+y^2 over the region 1<x^2+y^2<4.

    I did some working but it got far too complicated for the integral.

    Any help would be very nice.

    Thanks
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Nguyen View Post
    Hey, really stuck on this question.

    Integrate

    f(x,y,z)= \sqrt{3x^2+3y^2+z+1}

    over the surface given by the graph z=g(x,y)=x^2+y^2 over the region 1<x^2+y^2<4.

    I did some working but it got far too complicated for the integral.

    Any help would be very nice.

    Thanks
    first note that and covert to cylindrical coordinates to get

    dS=\sqrt{\left( \frac{\partial z}{\partial x}  \right)^2+\left( \frac{\partial z}{\partial y}  \right)^2 +1}=\sqrt{2}dA

    \int_{0}^{2\pi}\int_{1}^{2}\sqrt{3(r^2)+r^2+1}rdrd  \theta

    \int_{0}^{2\pi}\int_{1}^{2}\sqrt{4r^2+1}rdrd\theta
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  3. #3
    Junior Member
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    oh yes, thanks TheEmptySet, I see where my thinking was wrong. And thanks for the very fast reply!
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