1. ## double integrals, simple question about the limits

I understand how to do double integrals, but finding the limits of this region is confusing me... the question asks

Find the volume of the solid bounded by the cylinder y ^2 + z^ 2 = 1 and the planes x = 2y, x = 0, z = 0 in the first octant.

When I sketch this out, it goes infinitely doesn't it....
someone help clear the cobwebs from my brain?
Thanks

2. Originally Posted by plopony
I understand how to do double integrals, but finding the limits of this region is confusing me... the question asks

Find the volume of the solid bounded by the cylinder y ^2 + z^ 2 = 1 and the planes x = 2y, x = 0, z = 0 in the first octant.

When I sketch this out, it goes infinitely doesn't it....
someone help clear the cobwebs from my brain?
Thanks
No it does not, the cylinder is horizontal, the three planes cut the part of the cylinder in the first quadrant into two parts, one unbounded, and the other bounded. It is the bounded part that is the volume of interest.

CB