Q. $\int_{2}^{3}{\left\{ x \right\} dx}$ is equal to (where $\{ \bullet \}$ denotes fractional part of $x)$
A) $\frac{17}{2}$
B) $\frac{7}{2}$
C) $\frac{5}{2}$
D) $\frac{1}{2}$
Explanation
(d)
$\int_{2}^{3}{\left\{ x \right\} dx = \int_{2}^{3}{(x - \lbrack x\rbrack)dx =}\int_{2}^{3}{(x - 2)dx}}$
$= \left\lbrack \frac{x^{2}}{2} - 2x \right\rbrack_{2}^{3} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.