Use cylindrical coordinates to evaluate where T is the solid bounded by the cylinder and the planes and

Question

Use cylindrical coordinates to evaluate  where T is the solid bounded by the cylinder  and the planes  and

Quizplus · Accepted Answer

In cylindrical coordinates, the cylinder is defined by $r=11$ and $-3\leq z\leq 3$. The bounds for the angle $	heta$ are not given, so we can assume that $	heta$ ranges from $0$ to $2\pi$. Hence, the triple integral to evaluate the given expression is:
$$\iiint_T 11e^{x^2+y^2}\,dV = \int_0^{2\pi}\int_0^{11}\int_{-3}^3 11e^{r^2}r\,dz\,dr\,d	heta$$
Solving the integral yields the answer A.

Use Cylindrical Coordinates to Evaluate Where T Is the Solid