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Thread: Volume Integral

  1. December 16th 2009, 10:31 AM #1
    Aryth
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    Volume Integral

    Let R be the closed region in the xy-plane bounded by the graphs of y = x^2 and x = y^2. Let V be the solid bounded above by the surface z = 2x^2y whose base is the region R. Calculate the volume of V.
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  2. December 16th 2009, 12:29 PM #2
    tom@ballooncalculus
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    So the integral for R would be

    \displaystyle \int _0^1 (\sqrt{x} - x^2)\ dx

    ... so the volume integral is

    \displaystyle \int _0^1 \int_{x^2}^{\sqrt{x}} f(x,y)\ dy\ dx

    or...


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