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Math Help - cylindrical or spherical coordinates problem

  1. #1
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    cylindrical or spherical coordinates problem

    How to evaluate:
    ∫∫∫ xyz/(x^2+y^2)^1/2 dv
    E

    where E is the solid "quarter-cylinder" in the first octant bounded by a cylinder of radius a>o with axis long the z axis, the planes y=0,x=0,z=0 and z=b, wiht b>0.

    Thankyou very much!
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  2. #2
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    The best way to tackle this one is to change to cylindrical coordinates. So we'd get:

    <br /> <br />
\int_0^b \int_0^{\pi /2} \int_0^a \frac{(\rho cos\phi )(\rho sin\phi ) z}{\rho } \rho d\rho d\phi dz<br /> <br />

    <br /> <br />
\int_0^b zdz \int_0^{\pi /2} cos\phi sin\phi d\phi \int_0^a \rho ^2 d\rho<br /> <br />

    <br /> <br />
(\frac{b^2}{2})(\frac{1}{2})(\frac{a^3}{3})<br /> <br />

    <br /> <br />
\frac{a^3 b^2}{12}<br /> <br />
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  3. #3
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    thankyou!
    i got it so far, but how do u get p^2 for the third limit of integration? is that only be p???
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  4. #4
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    There's one p from x, on from y, one from the change to spherical coordinates (that comes with d phi), so that's p^3 in the numerator. Then in the denominator you have one p from (x^2+y^2)^1/2. So in total you have p^(3-1)=p^2
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