A) \[2\left( e+\frac{1}{e} \right)sq\,unit\]
B) \[0\text{ }sq\text{ }unit\]
C) \[2e\,sq\text{ }unit\]
D) \[\frac{2}{e}\,sq\text{ }unit\]
E) \[2\left( e-\frac{1}{e} \right)\,sq\text{ }unit\]
Correct Answer: D
Solution :
Required area\[=\int_{0}^{1}{(x{{e}^{x}}-x{{e}^{-x}})}\,dx\] \[=[x{{e}^{x}}-{{x}^{x}}+x{{e}^{-x}}+{{e}^{-x}}]_{0}^{1}\] \[=e-e+\frac{1}{e}+\frac{1}{e}=\frac{2}{e}sq\text{ }unit\]
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