Chapter 10 - Parametric Equations and Polar Coordinates - 10.4 Areas and Lengths in Polar Coordinates - 10.4 Exercises - Page 713: 30

$$A=(\frac{3\pi}{2}-4)$$

$$A=\int_{0}^{\pi/2}\frac{(1-cos\theta)^{2}}{2}d \theta=\int_{0}^{\pi/2}\frac{(1-2cos\theta+cos^{2}\theta)}{2}d \theta$$ Or, $$=\frac{1}{4}[3\theta-4sin\theta+\frac{1}{2}sin2\theta]_{0}^{\pi/2}$$ Hence, $$A=(\frac{3\pi}{2}-4)$$