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**1. Homework Statement**

$$f(x,y,z)=y$$ ; W is the region bounded by the plane ##x+y+z=2##, the cylinder ##x^2 +z^2=1##, and ##y=0##.

**2. Homework Equations**

**3. The Attempt at a Solution**

Since there is a plane of ##y=0##, I decided that my inner integral will be ##y=0## and ##y=2-x-z##. But after this I have a problem. I don't know how to proceed. How do I decide the bounds of ##x## and ##z##? Can I just use the function ##x^2+z^2=1##? If so, will it be $$\int_{-1}^1 \int_{-\sqrt(1-x^2)}^{\sqrt(1-x^2)} \int_ {0}^{2-x-z} y \,dy \, dz \, dx$$

Thanks.