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Homework Help: How to setup an integral in spherical coordinates for the volume of p = 2 sin O(theta

  1. Apr 13, 2005 #1
    Here is the problem:

    Find the volume of the region enclosed by the spherical coordinate surface [tex]\rho = 2 \sin\theta[/tex], using spherical coodinates for the limits of the integral.

    Here is what I have:

    I don't know if this is right, but here it is [tex]\int_{0}^{2\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\int_{0}^{2\sin\theta}\;\rho^2\;\sin\theta\;d\rho\;d\phi\;d\theta[/tex]
     
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  3. Apr 13, 2005 #2

    dextercioby

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    It looks okay.Did u plot it?Heh,u we use [itex] r,\varphi,\vartheta [/itex] as the spherical coordinates...:wink:

    Daniel.
     
  4. Apr 13, 2005 #3
    Whoops!

    I posted the wrong thing. Instead of [tex]2\sin\theta[/tex] for the first integrals upper limit, it should be [tex]2\sin\phi[/tex]?

    [tex]\int_{0}^{2\pi}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\int_{0}^{2\sin\phi}\;\rho^2\;\sin\theta\;d\rho\;d\phi\;d\theta[/tex]

    So confusing!

    Is that wrong now?

    The graph looks like a donut without the hole centered at the origin. I will post it shortly.
     
  5. Apr 13, 2005 #4

    dextercioby

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    No,it looks okay.

    Daniel.
     
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