Q. The area between the parabola $y = x^{2}$ and the line $y = x$ is
A) $\frac{1}{6}\ sq\ unit$
B) $\frac{1}{3}\ sq\ unit$
C) $\frac{1}{2}\ sq\ unit$
D) None of these
Explanation
(a)
The points of intersection of given curves are $O\ (0,0)$ and $P(1,1)$.
$\therefore Required\ area = \int_{0}^{1}x\ dx - \int_{0}^{1}x^{2}\ dx$
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${= \ \left\lbrack \frac{x^{2}}{2} - \frac{x^{3}}{3} \right\rbrack}_{0}^{1} = \frac{1}{6}sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.