I have two problems that are pretty similar:

1.Use a triple integral to find the volume of the solid bound by the parabolic cylinder $\displaystyle y=9x^2$ and the planes $\displaystyle z = 0, z = 9$, and $\displaystyle y = 5$.

I have been having issues finding the x bounds on this integral, but this is what I have tried: I set $\displaystyle y = 5 = 9x^2$ and solved for x, which gave me $\displaystyle x = + \sqrt {\frac {5} {9}}$ and $\displaystyle x = - \sqrt {\frac {5} {9}} $

I then had the integral:

$\displaystyle \int_{- \sqrt {\frac {5} {9}}}^{\sqrt {\frac {5} {9}}}\int_{9x^2}^{5}\int_{0}^{9} dzdydx$

I was just curious if this is right or not since I have been trouble with figuring out the bounds.

2.

The second question is this:

Find the volume of the solid enclosed by the paraboloids $\displaystyle z = (x^2 +y^2)$ and $\displaystyle z = 32 - (x^2+y^2) $

The bounds for z are there, but to find them for y and x could I set z = 0 and solve? So that $\displaystyle z = (x^2 + y^2)$ gives bounds for x and y that are 0 and then upper bounds for x and y that are $\displaystyle \sqrt {32}$.

And so the integral would be:

$\displaystyle \int_{0}^{\sqrt{32}}\int_{0}^{\sqrt{32}}\int_{(x^2 + y^2)}^{32 - (x^2 + y^2)} dzdydx$

Thanks ahead of time for the help.