Find the area enclosed between the curves $y = {log}_{e} (x + e), x = {log}_{e} (1 / y)$ & the x-axis

1 sq. units

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2 sq. units

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3 sq. units

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4 sq. units

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Solution

The correct option is B 2 sq. units
Area enclosed
$= \int_{1 - e}^{0} l n (x + e) d x + \int_{0}^{\infty} e^{- x} d x$
$= (x l n (x + e) - x) |_{1 - e}^{0} - e^{- x} |_{0}^{\infty}$
$= 2$

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