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  4. The area enclosed by the curves y= log e(x+ .e2), x= log e((2/y)) and x= log e 2, above the line y =1 is

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Q. The area enclosed by the curves $y=\log _e(x+$ $\left.e^2\right), x=\log _e\left(\frac{2}{y}\right)$ and $x=\log _e 2$, above the line $y =1$ is

JEE MainJEE Main 2022Application of Integrals

Solution:

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Required area is
$=\int\limits_{ e - e ^2}^0 \ln \left( x + e ^2\right)-1 dx +\int\limits_0^{\ln 2} 2 e ^{- x }-1 dx =1+ e -\ln 2$