Find the area bounded by the curve $y = e^{- x}$ , with the positive $X -$ axis and the $Y -$ axis .

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Solution

$Re q u i r e d a r e a = \infty \int 0 e^{- x} d x$
$= - {[e^{- x}]}_{0}^{\infty}$
$= - [e^{- \infty} - e^{- 0}]$
$= - [\frac{1}{e^{\infty}} - \frac{1}{e^{0}}]$
$= - [\frac{1}{\infty} - 1]$
$= - [0 - 1]$
$= 1$

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Find the area bounded by the curve y = $e^{- x}$ , the X -axis and the Y-axis.

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y = log x

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