Q. The volume of the solid generated by revolving the region bounded by $y = x^{2} + 1$ and $y = 2x + 1$ about $x$-axis is
A) $\frac{104\pi}{15}\ cu\ units\$
B) $\frac{42\pi}{15}\ cu\ units$
C) $\frac{52\pi}{15}\ cu\ units$
D) None of these
Explanation
(a)
On the solving the given equations of curves, we get $x = 0,2$
$\therefore Required\ volume = \pi\int_{0}^{2}{\lbrack(2x + 1)^{2} - \left( x^{2} + {1)}^{2} \right\rbrack dx}$
$= \pi\int_{0}^{2}{\left( {- x}^{4} + 2x^{2} + 4x \right)dx}$
$= \pi\left\lbrack - \frac{x^{5}}{5} + \frac{{2x}^{3}}{3} + \frac{{4x}^{2}}{2} \right\rbrack_{0}^{2} = \frac{104\pi}{15}\ sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.