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Math Help - bounded solid

  1. #1
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    bounded solid

    Let S be a solid bounded by the xy-plane, on the side by the cylinder x^2+y^2=2x and above by x^2+y^2+z^2=4.

    Set up a triple iterated integral in rectangular coordinates which represents the volume of the solid S.


    I know that the first integral is dx from 0 to 2, but how to obtain other?
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  2. #2
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    Quote Originally Posted by jacek View Post
    Let S be a solid bounded by the xy-plane, on the side by the cylinder x^2+y^2=2x and above by x^2+y^2+z^2=4.

    Set up a triple iterated integral in rectangular coordinates which represents the volume of the solid S.


    I know that the first integral is dx from 0 to 2, but how to obtain other?
    The inside integral is a surface to surface ( z=0 to the sphere) whereas the outer two integrals is a circle centered at (1,0) and radius 1 -
     <br />
\int_0^2\int_{-\sqrt{2x-x^2} }^{\sqrt{2x-x^2}} \int_0^{\sqrt{4-x^2-y^2}}dzdydx<br />

    although I think cylindrical polar coords would be the way to go. :-)
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