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Math Help - Spherical Coordinates Concept Question

  1. #1
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    Spherical Coordinates Concept Question

    I'm in the process of studying for a test next week and I have a review question I cannot answer. The problem asks to evaluate the integral by changing to spherical coordinates.

    I am only looking for what the actual integral would be in spherical coordinates, I don't actually need you to evaluate the integral.

    The triple integral in rectangular coordinates is:




    If you can, please provide an overview of what the sphere would look like.

    Thanks!
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  2. #2
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    Quote Originally Posted by 360modina View Post
    I'm in the process of studying for a test next week and I have a review question I cannot answer. The problem asks to evaluate the integral by changing to spherical coordinates.

    I am only looking for what the actual integral would be in spherical coordinates, I don't actually need you to evaluate the integral.

    The triple integral in rectangular coordinates is:




    If you can, please provide an overview of what the sphere would look like.

    Thanks!
    Everything you need is here: Spherical Coordinates -- from Wolfram MathWorld

    Almost everything ........ Note that your lower and upper integral terminals for r are 0 and a respectively (since the volume you're integrating over is a sphere of radius a).
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  3. #3
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    I ran through the problem as a normal sphere centered at (0, 0, 0) with a

    0\eqslantless\rho\eqslantless a
    0\eqslantless\theta\eqslantless\pi
    0\eqslantless\phi\eqslantless 2\pi

    and integrated in the order
    d\rho \ d\theta \ d\phi \

    and tacked a (\rho)^2 \sin \phi on the end to account for the spherical conversion.

    When I solve the problem I get with the mess of the (x^2*z+z...) spherical converted mess in there I end up with an answer of 0 and the same holds when I evaluate the original by hand in rectangular coordinates. Any thoughts?
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