iterated integral: volume enclosed by paraboloid, planes

[mathstresser]

Enclosed by the paraboloid z= x^2 +3y^2 and the planes x=0, y=1, y=x, and z=0.

I set up the integral to be (x^2+3y^2)dxdy, (1,?) and (0,y)

What else do evaluate the outside integral by?

 

[galactus]

It's been awhile since I messed with double or triple integrals, so check me out.

Try:

\(\displaystyle \L\\\int_{0}^{1}\int_{x}^{1}(x^{2}+3y^{2})dydx\)

or triple:

\(\displaystyle \L\\\int_{0}^{1}\int_{x}^{1}\int_{0}^{x^{2}+3y^{2}}dzdydx\)

See if you get the same answer.