Chapter 10.3, Problem 50ES

Determine whether the statement is true or false. Explain your answer.

The expression $\frac{1}{2}{{\displaystyle {\int }_{-\pi /4}^{\pi /4}\left(1-\sqrt{2}\cos \theta \right)}}^{2}d\theta$ computes the area enclosed by the inner loop of the limac̀§on $r=1-\sqrt{2}\cos \theta .$