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## Homework Statement

Integrate ##f(x,y,z) = z## over the region bounded by ##z = 0##, ##x^2 + 4y^2 = 4##, and ##z = x + 2##,

## Homework Equations

None.

## The Attempt at a Solution

I sketched the region in question, but my drawing is so terrible that I'm afraid it'll be little help to anybody who didn't draw it themselves. To describe the region in question, it is an elliptical cylinder (i.e. cylinder whose xy-cross section is an ellipse) and it is bounded by the xy-plane on the bottom and by the plane ##z = x + 2## on the top. Given this, I set up my integral as follows:

$$I = \int_{-2}^2 \int_{-2\sqrt{1 - y^2}}^{2 \sqrt{1 - y^2}} \int_0^{x + 2} z \ dz \ dx \ dy$$

Can anybody spot a mistake so far? I've attempted the entire problem, but I would like to make sure there isn't an issue so far before I tex it all up if possible. Thanks!