Use cylindrical coordinates to evaluate $\iiint _ { E } \sqrt { x ^ { 2 } + y ^ { 2 } } d V$ where E is the region that lies inside the cylinder $x ^ { 2 } + y ^ { 2 } = 25$ and between the planes $z = - 6 \text { and } z = 5$ . Round the answer to two decimal places.
A) $2878.33$
B) 2218.41
C) 2931.90
D) 2818.41
E) 2431.90

Question

Quizplus · Accepted Answer

The integral in cylindrical coordinates becomes $\int_{0}^{2\pi} \int_{0}^{5} \int_{-6}^{5} r^2 \, dz \, dr \, d\theta$. Evaluating this integral gives approximately 2878.33.

Use Cylindrical Coordinates to Evaluate ∭Ex2+y2dV\iiint _ { E } \sqrt { x ^ { 2 } + y ^ { 2 } } d V∭E​x2+y2​dV

Use Cylindrical Coordinates to Evaluate $\iiint _ { E } \sqrt { x ^ { 2 } + y ^ { 2 } } d V$