1. ## Volume Integral

Let R be the closed region in the xy-plane bounded by the graphs of $\displaystyle y = x^2$ and $\displaystyle x = y^2$. Let V be the solid bounded above by the surface $\displaystyle z = 2x^2y$ whose base is the region R. Calculate the volume of V.

2. So the integral for R would be

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

... so the volume integral is

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

or...

Spoiler:

Spoiler:

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

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