$\int\limits_0^{\frac{\pi}{2}} \sin ^2 x d x$ is equal to:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{\pi}{4}$
$\int\limits_0^{\frac{\pi}{2}} \sin ^2 x d x=\int\limits_0^{\frac{\pi}{2}}\frac{1}{2}-\frac{\cos 2x}{2}dx$
$=\left[\frac{x}{2}-\frac{\sin 2x}{4}\right]_0^{\frac{\pi}{2}}=\frac{\pi}{4}$