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Math Help - Surface Integrals

  1. #1
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    Surface Integrals

    Evaluate the following. (Give an exact answer.)
    Question is
    \iint\limits_{S} f(x,y,z) \, dS

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

    S: z=\sqrt{x^2+y^2}~,(x-1)^2+y^2\le1


    So after some work i arrive to to this.

    \sqrt{2}\int_0^2\int_{-\sqrt{1-(x-1)^2}}^{\sqrt{1-(x-1)^2}}\sqrt{x^2+y^2}\,dy\,dx

    which i then turn into sperical and get

    \sqrt{2} \int_0^{\frac{2}{\pi}}\int_0^1~r^2\,dr\,d\theta which equals 2\pi\frac{\sqrt{2}}{3}

    But my book example has a similar question as

    2 \int_0^{\frac{2}{\pi}}\int_0^1~r^2\,dr\,d\theta which equals \frac{4\pi}{3}

    Which is right? Why is theirs 2 and mine \sqrt{2} and are my limits right? Or is it all wrong Thanks for the help.
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  2. #2
    MHF Contributor
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    Re: Surface Integrals

    Hey tastylick.

    It might have something to do with the Jacobian: did you calculate this and if so what did you get?
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  3. #3
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    Re: Surface Integrals

    Surface Integrals-question-31.jpg

    My work is attached.
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