Q. The area bounded by the curves $\sqrt{x} + \sqrt{y} = 1$ and $x + y = 1$ is
A) 1/3 sq unit
B) 1/6 sq unit
C) $1/2\$sq unit
D) None of these
Explanation
(a)
Required area $= area\ of\ \mathrm{\Delta}\ AOB - \int_{0}^{1}{\left( 1 - \sqrt{x} \right)^{2}dx}$
[image:8_image10.jpeg]
$= \frac{1}{2} \times 1 \times 1 - \left\lbrack x - \frac{2x^{3/2}}{3} \right\rbrack_{0}^{1}$
$= \frac{1}{3}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.