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Math Help - Spherical Triple Integrals

  1. #1
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    Spherical Triple Integrals

    I am having trouble understanding how to come up with the PHI limit of integration in a triple integral. I know how to get rho? and Theta. Could someone please explain or give a link that could show how to determine the limits of integration for PHI? thanks
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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ur5pointos2slo View Post
    I am having trouble understanding how to come up with the PHI limit of integration in a triple integral. I know how to get rho? and Theta. Could someone please explain or give a link that could show how to determine the limits of integration for PHI? thanks
    It would be easier to explain if you could supply us with a particular problem that is stumping you.
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    Quote Originally Posted by Chris L T521 View Post
    It would be easier to explain if you could supply us with a particular problem that is stumping you.
    Sure, here is an example.

    Find the spherical coordinate limits for the integral that calculates the volume of the given solid and then evaluate the integral.

    The solid between the sphere rho=cos(phi) and the hemisphere rho = 2, z>=0

    I know theta and rho but do not understand how to find phi.

    So

    Int 0..2Pi Int ?..? Int cos(phi)..2 rho^2 sin(phi) drho dphi dtheta

    I hope that makes sense. I do not know how to use the latex.
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