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Q. Area bounded by the curves $y =e^{x}, y =e^{-x}$ and the straight line $x=1$ is (in sq. units)

KEAMKEAM 2014Application of Integrals

Solution:

Given curves are $y=e^{x}$ and $y=e^{-x}$.
The point of intersection is $e^{-x}=e^{x}$
$X=0$
Then, $Y=1$
image
So, the point of intersection is $(0,1)$.
$\therefore $ Area of bounded region $A B C$
$=\int\limits_{0}^{1}\left(y_{2}-y_{1}\right) d x=\int\limits_{0}^{1}\left(e^{x}-e^{-x}\right) d x$
$=\left[e^{x}+e^{-x}\right]_{0}^{1}=\left[e^{1}+e^{-1}-\left(e^{0}+e^{-0}\right)\right]$
$=\left[e+\frac{1}{e}-(1+1)\right]$
$=e+\frac{1}{e}-2$