Question

$\int_{0}^{\pi}{\sin^{2}xdx}$ is equal to

• A. π
• B. π/2
• C. 0
• D. None of these

Answer 1

Answer: (B)

π/2

Answer 2

$I = \frac { 1 } { 2 } \int _ { 0 } ^ { \pi } 2 \sin ^ { 2 } x d x = \frac { 1 } { 2 } \int _ { 0 } ^ { \pi } [ 1 - \cos 2 x ] d x$

⇒ $I = \frac{1}{2}\left\lbrack x - \frac{\sin 2x}{2} \right\rbrack_{0}^{\pi}$ ⇒ $I = \frac{1}{2}\lbrack\pi\rbrack = \frac{\pi}{2}$.