Write an Integral That Represents the Area of the Shaded $r = \cos 2 \theta \text { as }$

Multiple Choice

Write an integral that represents the area of the shaded region for $r = \cos 2 \theta \text { as }$ shown in the figure. Do not evaluate the integral.

A) $\int _ { - 5 \pi / 4 } ^ { - 3 \pi / 4 } ( \cos 2 \theta ) ^ { 2 } d \theta$
B) $\int _ { - 5 \pi / 2 } ^ { - 3 \pi / 2 } ( \cos 2 \theta ) ^ { 2 } d \theta$
C) $\frac { 1 } { 2 } \int _ { 3 \pi / 2 } ^ { 5 \pi / 2 } ( \cos 2 \theta ) ^ { 2 } d \theta$
D) $\frac { 1 } { 2 } \int _ { - 5 \pi / 4 } ^ { - 3 \pi / 4 } ( \cos 2 \theta ) ^ { 2 } d \theta$
E) $\frac { 1 } { 2 } \int _ { 3 \pi / 4 } ^ { 5 \pi / 4 } ( \cos 2 \theta ) ^ { 2 } d \theta$