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Q.
Area of the region bounded by $y = e^x , y = e^{-x} , x = 0 $ and $x = 1$ in sq. units is
Application of Integrals
Solution:
$y = e ^{ x }, y = e ^{- x }$
Then, area bounded by these two curves s given by $A =\int_{0}^{1}\left( e ^{ x }- e ^{- x }\right) d x =\int_{0}^{1} e ^{ x } d x -\int_{0}^{1} e ^{- x } dx$
$=\left( e ^{1}- 1 \right)+ 1 \left( e ^{-1}- 1 \right)$
$= e + e ^{- 1 }- 2$
$=\left(\sqrt{ e }-\frac{1}{\sqrt{ e }}\right)^{2}$ sq units.