Area of a Paraboloid inside a Cylinder Find the area of the part of the paraboloid $x=y^2+z^2$ that is inside the cylinder $y^2+z^2=9$. I'm not sure how to set up the integral to compute this. Thanks.

The paraboloid and cylinder intersect at $x=9$, so the height of the paraboloid is $h=9$ then find the surface area by integrating:

$$ A=\int\int \sqrt{1+(2y)^2+(2z)^2} $$

which you need to convert to polar coordinates...