Q. The area bounded by the curves $y = x^{3},\ y = x^{2}$ and the ordinates $x = 1,\ x = 2$ is
A) $\frac{17}{12}$
B) $\frac{12}{13}$
C) $\frac{2}{7}$
D) $\frac{7}{2}$
Explanation
(a)
Required area $= \int_{1}^{2}{\left( x^{3} - x^{2} \right)dx}$
$= \left( \frac{x^{4}}{4} - \frac{x^{3}}{3} \right)_{1}^{2}$
$= \left( 4 - \frac{8}{3} \right) - \left( \frac{1}{4} - \frac{1}{3} \right) = \frac{17}{22}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.