Q. The area bounded by $y = \sin^{- 1}{\ x = \frac{1}{\sqrt{2}}}$ and $x$-axis is
A) $\left( \frac{1}{\sqrt{2}} + 1 \right)\ sq\ unit$
B) $\left( 1 - \frac{1}{\sqrt{2}} \right)\ sq\ unit$
C) $\frac{\pi}{4\sqrt{2}}\ sq\ unit$
D) $\left( \frac{\pi}{4\sqrt{2}} + \frac{1}{\sqrt{2}} - 1 \right)\ sq\ unit$
Explanation
(d)
Required area
[image:8_image6.jpeg]
$= Area\ of\ recangle\ OABC - Area\ of\ curve\ OABO$
$= \frac{\pi}{4\sqrt{2}} - \int_{0}^{\pi/4}{\sin{y\ dy}}$
$= \frac{\pi}{4\sqrt{2}} + \left\lbrack \cos y \right\rbrack_{0}^{\pi/4} = \left\lbrack \frac{\pi}{4\sqrt{2}} + \left\{ \frac{1}{\sqrt{2}} - 1 \right\} \right\rbrack\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.