Question

The value of the integral ${\int }_{-2}^2(1+2\sin x)e^{|x|}dx$ is equal to

• A. $0$
• B. $e^2-1$
• C. $2(e^2-1)$
• D. $1$

Answer 1

Answer: (C)

$2(e^2-1)$

${\int }_{-2}^2(1+2\sin x)e^{|x|}dx$

$={\int }_{-2}^2{e}^{|x|}dx+2{\int }_{-2}^2\sin x{e}^{|x|}dx$
(Since, first function is even and second function is odd)

$=2{\int }_0^2{e}^{x}dx+2,0=2[e^x{]}_0^2=2(e^2-1)$