Q. The area bounded by $y = \ \sin^{- 1}x,\ x = \frac{1}{\sqrt{2}}$ and $x$-axis is
A) $\left( \frac{1}{\sqrt{2}} + 1 \right)\ sq\ units$
B) $\left( 1 - \frac{1}{\sqrt{2}} \right)\ sq\ uints\$
C) $\frac{\pi}{4\sqrt{2}}\ sq\ units$
D) $\left( \frac{\pi}{4\sqrt{2}} + \frac{1}{\sqrt{2}} - 1 \right)\ sq\ units$
Explanation
(d)
Required area
= area of rectangle $OABC -$ area of curve $OBCO$
[image:8_image62.jpeg]
$= \frac{\pi}{4\sqrt{2}} - \int_{0}^{\frac{\pi}{4}}{\sin{y\ dy}}$
$= \frac{\pi}{4\sqrt{2}} + \lbrack\cos{y\rbrack_{0}^{\frac{\pi}{4}}}$
$= \left\lbrack \frac{\pi}{4\sqrt{2}} + \left( \frac{1}{\sqrt{2}} - 1 \right) \right\rbrack\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.