Evaluate the double integral below. $$\int _ { 0 } ^ { \frac { \pi } { 5 } } \int _ { 0 } ^ { 5 } r ^ { 5 } \sin \theta \cos \theta d r d \theta$$
A) $\frac { 1202 } { 1203 } \sin \frac { \pi } { 5 }$
B) $\frac { 15625 } { 12 } \sin \frac { \pi } { 5 }$
C) $\frac { 12 } { 15625 } \sin ^ { 2 } \frac { \pi } { 5 }$
D) $\frac { 15625 } { 12 } \sin ^ { 2 } \frac { \pi } { 5 }$
E) $\frac { 1 } { 12 } \sin ^ { 2 } \frac { \pi } { 5 }$

Question

Quizplus · Accepted Answer

The integral evaluates to $\frac { 15625 } { 12 } \sin ^ { 2 } \frac { \pi } { 5 }$ after integrating $r^5$ with respect to $r$ and $\sin \theta \cos \theta$ with respect to $\theta$.

Evaluate the Double Integral Below ∫0π5∫05r5sin⁡θcos⁡θdrdθ\int _ { 0 } ^ { \frac { \pi } { 5 } } \int _ { 0 } ^ { 5 } r ^ { 5 } \sin \theta \cos \theta d r d \theta∫05π​​∫05​r5sinθcosθdrdθ

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