Question

Compute the volume of the solid bounded by xz-plane, the yz-plane, the
xy-plane, and the planes x = 1, y = 1, and the surface z = x2 + y4.

Answer 1

The solid you're dealing with is the region of points \((x,y,z)\) under the surface \(z=x^2+y^4\) that looks like this:
http://www.wolframalpha.com/input/?i=Plot%5Bx%5E2%2By%5E4%2C%7Bx%2C0%2C1%7D%2C%7By%2C0%2C1%7D%5D

So, if we let \(E\) be the solid, then you have
\[E:=\left\{(x,y,z)~:~0\le x\le1,~~0\le y\le1,~~0\le z\le x^2+y^4\right\}\]
The integral representing \(E\)'s volume would be
\[\int\int\int_EdV=\int_0^1\int_0^1\int_0^{x^2+y^4}dz~dy~dx\]
A fairly simple integral to compute.