Q. $\int_{0}^{3}{|x^{3} + x^{2} + 3x|dx}$ is equal to
A) $\frac{171}{2}$
B) $\frac{171}{4}$
C) $\frac{170}{4}$
D) $\frac{170}{3}$
Explanation
(b)
$\int_{0}^{3}{|x^{3} + x^{2} + 3x|dx} = \int_{0}^{3}{(x^{3} + x^{2} + 3x)dx}$
$= \left\lbrack \frac{x^{4}}{4} + \frac{x^{3}}{3} + \frac{3x^{2}}{2} \right\rbrack_{0}^{3}$
$= \frac{81}{4} + \frac{27}{3} + \frac{27}{2} = \frac{171}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.