_0^ ^2 x ,dx is equal to - Vidyadip

MCQ

$\int_0^\pi {{{\sin }^2}x\,dx} $ is equal to

A
$\pi $
✓
$\frac{\pi }{2}$
C
$0$
D
None of these

✓

Answer

Correct option: B.

$\frac{\pi }{2}$

b
(b) $I = \int_0^\pi {{{\sin }^2}x\,dx = 2\int_0^{\pi /2} {{{\sin }^2}x\,dx} } $,

$\{\because \,\,\int_{0}^{2a}{f(x)=2\int_{0}^{a}{f(a-x)dx}}$, if $f(2a - x) = f(x) \}$

$I = 2 \times \frac{1}{2} \times \frac{\pi }{2} = \frac{\pi }{2}$.

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