Find the area of the specified region.
-Inside the limacon r = 9 + 6 sin $\theta$
A) 99$\pi$
B) 198$\pi$- 108
C) 99$\pi$+ 108
D) 198$\pi$

Question

Quizplus · Accepted Answer

The area inside the limacon $r = 9 + 6\sin(\theta)$ can be found using the formula for the area of a polar curve, $A = \frac{1}{2}\int_{a}^{b} r^2 d\theta$. For a complete limacon, we integrate from $0$ to $2\pi$. Substituting $r = 9 + 6\sin(\theta)$ into the formula, we get $A = \frac{1}{2}\int_{0}^{2\pi} (9 + 6\sin(\theta))^2 d\theta$. Simplifying and integrating, we find that the area is $99\pi$.

Find the Area of the Specified Region θ\thetaθ A) 99 π\piπ B) 198

Find the Area of the Specified Region $\theta$ A) 99 $\pi$ B) 198