Q. $\int_{1}^{2}{e^{x}\left( \frac{1}{x} - \frac{1}{x^{2}} \right)dx}$ is equal to
A) $e - \frac{e^{2}}{2}$
B) $\frac{e^{2}}{2} - e$
C) $\frac{e^{2}}{2} + e$
D) $\frac{e^{2}}{2} - 2$
Explanation
(b)
$\int_{1}^{2}e^{x}\left( \frac{1}{x} - \frac{1}{x^{2}} \right)dx = \left\lbrack \frac{1}{x}e^{x} \right\rbrack_{1}^{2} + \int_{1}^{2}{\frac{e^{x}}{x^{2}}dx - \int_{1}^{2}{\frac{e^{x}}{x^{2}}dx}}$
$= \frac{e^{2}}{2} - e$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.