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About LinkBacksLet 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.
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.
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:
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Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
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