Question

This is another triple integration problem; I don't have an issue necessarily calculating it, but I don't understand, from the given surfaces, why the object is described the way it is in the solution. One moment.

Answer 1

\[\int\limits_{}^{}\int\limits_{}^{}\int\limits_{}^{}z^{2}y \ dV, where:\]

Answer 2

The area concerned is bounded by the surfaces z = y from above, z = 0 from below, and x^2 + y^2 = 4.

The specific thing I don't understand is that in the solution, it says that in polar coordinates, the range of theta is from zero to 2pi. The way I understand this, if the region is *above* z = 0 and *below* z = y and cut off by the cylinder x^2 + y^2 = 4, the region should look *exactly* like an orange slice. Let me plot these projected into the yz planes (and others) to describe what I imagine.