Overview
QUESTION:
Non-circular cylinder. A solid right (non-circular) cylinder has its base R in the xy-plane and is bounded above by the paraboloid [Image unavailable: LaTeX: z=x^2+y^2]z=x2+y2 . The cylinder's volume is
[Image unavailable: LaTeX: V=\int_0^1\int_0^y\left(x^2+y^2\right)dxdy+\int_1^2\int_0^{2-y}\left(x^2+y^2\right)dxdy]
Sketch the base region R and express the cylinder's volume as a single iterated integral with the order of integration reversed. Then evaluate the integral to find the volume