Compute the volume of the solid bounded by the plane xzxz, the plane yzyz, the plane xyxy, the planes x=1x=1 y y=1y=1, and the surface z=x2+y4z=x^{2}+y^{4}

Problem: Compute the volume of the solid bounded by the plane xzxz, the plane yzyz, the plane xyxy, the planes x=1x=1 y y=1y=1, and the surface z=x2+y4z=x^{2}+y^{4}.

Solution:

First, I have plotted this:

And this is the double integral defined:

∫10∫10(x2+y4)dxdy\int_{0}^{1}\int_{0}^{1}(x^{2}+y^{4})dxdy

I’m not sure if that double integral computes the volume for the bounded solid…

I want to know how to bound solids between different functions in a general way.

Ideas, suggestions, etc.?

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Hello! That is a very nice drawing…and the integral seems to be correct.
– DonAntonio
2 days ago

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