Use a double integral to find the area of the region enclosed by one loop of the curve $r = \cos 2 \theta$ .
A)1
B) $\frac { \pi } { 4 }$
C) $\frac { \pi } { 16 }$
D) $\frac { 46 \pi } { 27 }$
E) $\frac { 5 } { 2 }$
F) $\frac { 1 } { 2 }$
G) $\frac { \pi } { 8 }$
H) $\frac { 46 } { 27 }$

Question

Use a double integral to find the area of the region enclosed by one loop of the curve $r = \cos 2 \theta$ .
A)1
B) $\frac { \pi } { 4 }$ 
C) $\frac { \pi } { 16 }$
D) $\frac { 46 \pi } { 27 }$ 
E) $\frac { 5 } { 2 }$
F) $\frac { 1 } { 2 }$ 
G) $\frac { \pi } { 8 }$ 
H) $\frac { 46 } { 27 }$

Quizplus · Accepted Answer

The area of one loop of the curve $r = \cos 2 \theta$ is given by $\frac{1}{2} \int_{-\pi/4}^{\pi/4} (\cos 2\theta)^2 \, d\theta$, which evaluates to $\frac{\pi}{8}$.

Use a Double Integral to Find the Area of the Region