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Math Help - am i doing this right? triple integral, spherical coordinates

  1. #1
    Junior Member
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    am i doing this right? triple integral, spherical coordinates

    so what i am concerned about here is simply setting up the correct bounds. if i do that right, i know how to integrate just fine.
    i need to find the bounds for the hemisphere given by x^2 + y^2 + z^2 = 16 and z>=o
    solving for z, i get z= root(6-x^2-y^2. )

    i believe that is a sphere, right?

    so a sphere that lies above (or with the bottom directly on xy plane) with radius of 4.

    so my bounds for 0<roe<4

    theta is the angle on the xy plane, and since it's a sphere, it goes all the way around, from 0 to 2pi.

    and for phi, that goes from the z axis down to the y axis. and since it can't go below the y axis into the negative z, (because z>=0), that would mean the max is pi/2.

    so is that correct for my bounds?

    0<roe<4
    0<theta<2pi
    0<phi<pi/2

    i don't quite understand this, but i'm trying to picture this 3 dimensionally. anyway, if i am wrong, could someone point out where i am going wrong? thank you
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  2. #2
    A Plied Mathematician
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    Everything looks good to me, except that you should spell it rho, not roe.
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  3. #3
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    ha good call. thanks for the response!
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