Evaluate the following Integral: ∫x e^|x| dx, x ∈ [-2, 2]

Question

Evaluate the following Integral:

\(\int\limits_{-2}^{2} \)x e^|x| dx

Answer 1

 \(\int\limits_{-2}^{2} \)x e^|x|

\(= \int\limits_{-2}^0\) x e^-xdx + \( \int\limits_{0}^2\)x e^x dx

Let’s Say I = I₁ + I₂

And, I₁ =  \(= \int\limits_{-2}^0\) x e^-x dx

Using Integration By parts

For I₂ = \(\int\limits_{0}^{2} \)x e^xdx

Using Integration By parts

Hence, 0