Q. The area bounded by the curve $y = \sin^{2}x$ and lines $x = \frac{\pi}{2}$, $x = \pi$ and $x$-axis is
A) $\frac{\pi}{2}\ sq\ unit$
B) $\frac{\pi}{4}\ sq\ unit$
C) $\frac{\pi}{8}\ sq\ unit$
D) None of these
Explanation
(b)
Required area $A = \int_{\pi/2}^{\pi}{\sin^{2}{x\ dx}}$
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$= \frac{1}{2}\int_{\pi/2}^{\pi}{(1 - \cos{2x)dx}}$
$= \frac{1}{2}\left\lbrack x - \frac{\sin{2x}}{2} \right\rbrack_{\pi/2}^{\pi}$
$= \frac{\pi}{4}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.