Q. $\int_{- 1/7}^{20/7}e^{5\{ x\}}dx$ is equal to (where $\{ \bullet \}$ denotes fractional part of $x)$
A) $\frac{3}{5}\left( e^{5} \right)$
B) $\frac{3}{5}\left( e^{5} - 1 \right)$
C) $\frac{3}{5}$
D) None of these
Explanation
(b)
$\int_{- 1/7}^{20/7}{e^{5\{ x\}}dx =}\int_{- 1/7}^{3 - \frac{1}{7}}{e^{5\{ x\}}dx}$
$= 3\int_{0}^{1}{e^{5\{ x\}}dx = 3\int_{0}^{1}{e^{5x}dx\ \ \ \ \ (\left\{ x \right\} = x\ as\ 0 \leq x < 1)}}$
$= 3\left\lbrack \frac{e^{5x}}{5} \right\rbrack_{0}^{1} = 3\left( \frac{e^{5} - 1}{5} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.