# Thread: volume bounded by surface

1. ## volume bounded by surface

A volume in the first octant of space is bounded above by the surface z=4-(x^2), below by the plane z=0, and laterally by x=0 and the cylinder y=2x-(x^2). Compute the volume.

2. Originally Posted by ratedmichael
A volume in the first octant of space is bounded above by the surface z=4-(x^2), below by the plane z=0, and laterally by x=0 and the cylinder y=2x-(x^2). Compute the volume.
$\iint_A \int_0^{4-x^2} dz ~dA$ where $A$ is the region of integration made by the parabola $y=2x-x^2$.

3. There's various ways to set it up.

triple integral:

$\int_{0}^{2}\int_{0}^{2x-x^{2}}\int_{0}^{4-x^{2}}dzdydx$

Double integral:

$\int_{0}^{2}\int_{0}^{2x-x^{2}}(4-x^{2})dydx$

Try it in cylindrical or spherical.

4. ## Tough Solution

Polar necessary?