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Math Help - integral

  1. #1
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    integral

     \int_{0}^{\pi/2} \int_{0}^{\pi/2} \int_{1}^{2} \rho^{2} \sin \phi \ d \rho \ d \phi \ d \theta

    I evaluated it and got  0 .

    So what type of solid is this?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by shilz222 View Post
     \int_{0}^{\pi/2} \int_{0}^{\pi/2} \int_{1}^{2} \rho^{2} \sin \phi \ d \rho \ d \phi \ d \theta

    I evaluated it and got  0 .

    So what type of solid is this?
    i did not get zero, and you should not either. this integral is giving the volume of a solid. it gives the volume of the region in the first octant bounded between a sphere of radius 1 and a sphere of radius 2, both centered at the origin.
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  3. #3
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    Quote Originally Posted by shilz222 View Post
    So what type of solid is this?
    Think of this. Everything from the outside to the grey thing. Except in this solid it is 1/2 the size of semi-earth. So divide that shape into two equal part to get your solid.
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