Question

The value of integral $\int x{e}^{-|x|}dx$ will be

• A. $(x-1)e^x+C$ for $x\in [-2\pi ,0]$
• B. $-\left(x\right)e^{-x}+C$ for $x\in [0,2\pi ]$
• C. $\left(x\right)e^x+C$ for $x\in [-2\pi ,0]$
• D. None of these

Answer 1

Answer: (D)

None of these

If $x$ is positive then $\int x{e}^{-|x|}dx=\int x{e}^{-x}dx=-x{e}^{-x}+\int e^{-x}dx=-x{e}^{-x}-e^{-x}=-e^{-x}(x+1)$

Therefore the correct option is $D$