Q. If $f(x) = x(x - 1),\ 0 \leq x \leq 1$ and $f(x + 1) = f(x),\ \forall\ x \in R,$ then $|\int_{2}^{4}{f(x)dx|\ }$is
A) 1 sq unit
B) $\frac{1}{3}$ sq unit
C) $\frac{2}{3}$ sq unit
D) $\frac{1}{6}$ sq unit
Explanation
(b)
Graph of $y = f(x)$ will be of the following form. Form the graph we can observe that period of $f(x)$ is 1 unit.
[image:7_image2.emf]
$\therefore\ \left| \int_{2}^{4}{f(x)dx} \right| = 2\left| \int_{0}^{1}{x(x - 1)dx} \right| = \frac{1}{3}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.