I need to compute the volume of the 3-D domain bounded below and by the sides by the positive orthant $x\ge0, y\ge0, z\ge0$, bounded from the top by the paraboloid $z=x^2+y^2+9$ and bounded on the side by the parabolic cylinder $y=4-x^2$.
So far, I'm having trouble envisioning this region of integration and even getting started setting up my limits of integration.
Here's the region - its under the paraboloid and bounded to the side by $y=4-x^2$, so the bounds for integration are: $$ 0\le x \le 2 \\ 0 \le y \le 4-x^2 \\ 0 \le z \le x^2 + y^2 + 9$$