Evaluate the double integral below. $$\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 } 2 r ^ { 5 } \sin \theta d r d \theta$$
A) $3 \pi$
B) 0
C) $\pi$
D) $2 \pi$
E) $\frac { \pi } { 2 }$

Name: Evaluate the double integral below. \[\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 } 2 r ^ { 5 } \sin \theta d r d \theta\] A) $3 \pi$ B) 0 C) $\pi$ D) $2 \pi$ E) $\frac { \pi } { 2 }$
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Question

Quizplus · Accepted Answer

The integral of $\sin \theta$ over the interval $[0, 2\pi]$ is zero, making the entire double integral zero.

Evaluate the Double Integral Below ∫02π∫032r5sin⁡θdrdθ\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 } 2 r ^ { 5 } \sin \theta d r d \theta∫02π​∫03​2r5sinθdrdθ

Evaluate the Double Integral Below $\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 3 } 2 r ^ { 5 } \sin \theta d r d \theta$