Hi there. I have this problem with double integral, which says: calculate using a double integral the volume limited by the given surfaces:

,

Its a cylinder cut by a plane.

At first I've did this integral:

The thing is that when I solve this the terms null themselves and it gives zero. There is evidently something that I'm doing wrong, I've realized that I'm taking off a half of the volume to the other, so I think I'm defining one part of the area over which I'm making the integral as negative. Is this true? And the thing is: How do I solve this properly? I've introduced this double integral into mathematica and it solved it and gave

. So, its clear I'm doing something wrong

I also thought on trying other way:

But it gets more complicated that way.

Bye there, and thanks for helping.