I love polar coordinates, but not very familiar with them...
Here is the problem:
Use polar coordinates to find the volume of the given solid.
Below the paraboloid z = 36 - 9x^2 - 9y^2 and above the xy-plane.
the paraboloid can be rewritten as x^2+y^2 = 4
in this case, i thought the limits in polar coordinates would be:
0 <= theta <= pi
0 <= r <= 2
since the radius of the circle is 2 and is only in the first two quadrants.
since r = x^2 + y^2.... it is just the double integral of r^2 dr d-theta. in that case i got my final answer to be 8/3(pi).
Where did I get my reasoning wrong? Thanks