Question

Area bounded by $y=|1-e^{|x|}|$ and $y=0$ for $x\in [-1,1]$ is

• A. $e-2$
• B. $e(e-2)$
• C. $2(e-2)$
• D. None of these

Answer 1

The correct option is C $2(e-2)$


Area $=\underset{-1}{\overset{1}{\int }}|1-e^{|x|}|dx$
$=2\underset{0}{\overset{1}{\int }}-(1-e^x)dx(\because 1-e^{|x|}\le 0\forall x\in [0,1])$
$=2\underset{0}{\overset{1}{\int }}(e^x-1)dx$
$=2[e^x-x{]}_0^1=2[e-1-1]=2(e-2)$