Q. Area bounded by the curves $y = x^{2}$ and $y = 2 - x^{2}$ is
A) 8/3 sq units
B) 3/8 sq units
C) 3/2 sq units
D) None of these
Explanation
(a)
Required area $= 2$ area of curve $OABO$
[image:8_image3.jpeg]
$= 2\int_{0}^{1}{\left\lbrack \left( 2 - x^{2} \right) - \left( x^{2} \right) \right\rbrack dx}$
$= 2\int_{0}^{1}{\left( 2 - {2x}^{2} \right)dx\ }$
$= 4\left\lbrack x - \frac{x^{3}}{3} \right\rbrack_{0}^{1} = \frac{8}{3}sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.