Question

The value of the integral ${\int }_{-\pi /2}^{\pi /2}\sqrt{1-{\cos }^2\theta }d\theta$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $-2$

Answer 1

Answer: (C)

Let $I={\int }_{-\pi /2}^{\pi /2}\sqrt{1-{\cos }^2\theta }d\theta$
$={\int }_{-\pi /2}^{\pi /2}|\sin \theta |d\theta$
$=2{\int }_0^{\pi /2}\sin \theta d\theta$
$=2[-\cos \theta {]}_0^{\pi /2}$
$=2\left(-\cos \frac{\pi }{2}+\cos 0^o\right)$
$=2(1)=2$