Free Area enclosed by polar graphs challenge Practice Problems • Learn To Be

The

\blue{\text{shaded region}}

below is bounded by the circles

\red{r=2}

and

\purple{r=4\cos\theta}

.

Which of these expressions represent the area of the region?

Choose all answers that apply:

A
$\displaystyle \dfrac{2\pi}3 + 8\int_{-\pi/3}^{\pi/3} \cos^2\theta \, d\theta$
B
$\displaystyle \dfrac{4\pi}3 + 8\int_{\pi/3}^{2\pi/3} \cos^2\theta \, d\theta$
C
$\displaystyle \dfrac{4\pi}3 + 16\int_{\pi/3}^{\pi/2} \cos^2\theta \, d\theta$
D
$\displaystyle \dfrac{2\pi}3 + 16\int_{0}^{\pi/3} \cos^2\theta \, d\theta$

Area enclosed by polar graphs challenge