Volume Integral

**Aryth** · Dec 16th 2009, 11:31 AM

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.

**tom@ballooncalculus** · Dec 16th 2009, 01:29 PM

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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