1. ## polar coordinate

Find the area of the region inside: $r = 8 \sin \theta$ but outside $r = 4$

2. First find the points of intersection.

So $8 \sin \theta = 4, \ \sin \theta = \frac{1}{2}$ or $\theta = \frac{\pi}{6}, \ \frac{5 \pi}{6}$.

So $A = \frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{5 \pi}{6}} (8 \sin \theta)^2 \ d \theta - \frac{1}{2} \int_{\frac{\pi}{6}}^{\frac{5 \pi}{6}} 16 \ d \theta$.

3. how did you get 81 in the 2nd integral?

4. it should be $16$.

5. Originally Posted by viet
Find the area of the region inside: $r = 8 \sin \theta$ but outside $r = 4$

Maple-generated graph

plot([8*sin(theta),4],theta=0..2*Pi,coords=polar,thickness=3,color=[red,blue]);