Q. The area between the curves $y = {xe}^{x}\ and\ y = {xe}^{- x}$ and line $x = 1,\$in square unit, is
A) $2\left( e + \frac{1}{e} \right)\ sq\ units$
B) 0 sq unit
C) $2e$ sq units
D) $\frac{2}{e}\ sq\ unit$
Explanation
(d)
$Required\ area = \int_{0}^{1}{{xe}^{x}\ \ dx - \int_{0}^{1}{{xe}^{- x}\ \ \ dx}}$
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$= \lbrack{xe}^{x} - e^{x}\rbrack_{0}^{1} - \lbrack - {xe}^{- x}e^{- x}\rbrack_{0}^{1} = \frac{2}{e}\ sq\ unit$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.