Chapter 6, Problem 4AAE

a)

To determine

Show that the integral ${\displaystyle \underset{0}{\overset{\alpha }{\int }}\sqrt{1+{\cos }^2\theta }}d\theta >\sqrt{{\alpha }^2+{\sin }^2\alpha }$ for the interval of $0<\alpha \le \frac{\pi }{2}$.

b)

To determine

Generalize the answer ${\displaystyle \underset{0}{\overset{\alpha }{\int }}\sqrt{1+{\cos }^2\theta }}d\theta >\sqrt{{\alpha }^2+{\sin }^2\alpha }$.