Volume of a solid: y=x^2 and the planes z=3y, z=2+y

[calchere]

Find the volume of the solid by subtracting two volumes.

The solid enclosed by the parabolic cylinder y=x^2 and the planes z=3y, z=2+y

I'm having a bit of trouble setting up the problem. I think it should look something like:
∫∫(3y) dydx - ∫∫ (2+y) dydx

I'm not sure what the boundaries for the x and y integrals are.
I think the low boundary for both is 0, but i'm not sure of how to get the upper boundaries.

 

[calchere]

I still can't seem to figure out the limits of the x and y integrals. I'm thinking that the x integral limit should be (0 to 1) and the y integral should be (0 to x^2).

Any help please.
Thanks

 

[galactus]

It appears no one has bitten, so I will. I believe this is the correct setup(I hope):


\(\displaystyle \L\\\int_{-1}^{1}\int_{x^{2}}^{3}[3y-(2+y)]dydx\)

Here's a 3D graph. I hope it's a little help to see what your region looks like.