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Math Help - Volume Integral

  1. #1
    Super Member Showcase_22's Avatar
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    Volume Integral

    Find the volume of the region in \mathbb{R}^3 that is bounded by the paraboloid z=x^2+y^2, the cylinder x^2+y^2=1 and the plane z=0.

    Do I need to work out \int_0^1 \int_0^{\sqrt{1-x^2}} \int_0^{x^2+y^2}~dz~dy~dx?
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Notice the region of integration is the unit circle so you would have to multiply

    by 4

    However it is easier i you use cylindrical coordinates

    See attachment
    Attached Thumbnails Attached Thumbnails Volume Integral-clndrcl.jpg  
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