Originally Posted by

**lllll** I'm having a bit of trouble finding the the bounds for the following problems.

1) $\displaystyle z=x^2+3y^2$ and the planes $\displaystyle x = 0, \ y=1, \ y=x, \ z=0$

since z will be a paraboloid and bounded by those constraints I'm thinking I would have $\displaystyle \int_{x=0}^{x=1} \int _{y=x}^{y=1} x^2+3y^2 \ dy \ dx$

2) $\displaystyle z= x^2 , \ y=x^2$ and the planes $\displaystyle z=0, \ y=4$

so I get the graph that's in the attachment, now if I take those constraints into account then I would simple have something above the xy plane and to the right of the xz plane, therefore I would think that my integral would be:

$\displaystyle \int_{x=-2}^{x=2} \int_{y=x^2}^{y=4} x^2 \ dy \ dx$