Q. $\int_{0}^{1}{\left\{ x \right\} d\{ x\}}$ is equal to (where $\{ \bullet \}$ denotes fractional part of $x)$
A) 0
B) 1
C) $\frac{1}{2}$
D) None of these
Explanation
(c)
$\left\{ x \right\} = x,\ 0 \leq x < 1$
$I = \int_{0}^{1}{x\ dx = \left\lbrack \frac{x^{2}}{2} \right\rbrack_{0}^{1} = \frac{1}{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.