Question

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

Answer 1

Given function is

$y=e^{-x}$

When x = 0, y = $e^{-0}$ = 1

x increases vlaue of y deceases and only at

x= $\infty$, y =0

So, the required area can be founded out by integrating the function from 0 to $\infty$.

$\therefore$ Area = ${\int }_{\infty }^0{e}^{-x}dx$

=- ${[e-e^{-x}]}_0$

=-[0-1]=1