Question

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

Answer 1

$\Rightarrow (y=e^{-x})$ is the given curve
It cuts x - axis at y = 0
$\Rightarrow e^{-x}=0\Rightarrow \frac{1}{e^x}=0$
$\Rightarrow x\to \infty$
It cuts y - axis at x = 0
$\therefore y=e^0=1\Rightarrow (0,1)$
$\therefore {\int }_0^{\infty }{e}^{-x}dx=-e^{-x}{|}_0^{\infty }=-[\frac{1}{e^{\infty }}-e^0]$
$=-(0-1)=1$