Find the area of the specified region.
-Shared by the circle r = 8 and the cardioid r = 8(1 + sin $\theta$)
A) 16(5$\pi$ - 8)
B) 64
C) 0
D) 16(5$\pi$ +8)

Question

Quizplus · Accepted Answer

The area shared by the circle $r = 8$ and the cardioid $r = 8(1 + \sin \theta)$ can be found by integrating the difference in their radial functions over the range of $\theta$ where they overlap. The area of the region that is inside both the circle and the cardioid is given by the integral of the difference between the two radii, from the points where they intersect. The correct formula involves subtracting the area of the cardioid from the circle and involves constants and $\pi$, leading to the answer $16(5\pi - 8)$.

Find the Area of the Specified Region θ\thetaθ ) A) 16(5 π\piπ

Find the Area of the Specified Region $\theta$ )
A) 16(5 $\pi$