Answer
40000*(1-(e$^{-2}$)*ln(7/2$)\approx$43,329
Work Step by Step
$\int_{-5}^{5}$$\int_{-2}^{0}$$\frac{(10000e^{y})}{(1+\lvert \frac{x}{2}\rvert)}$dydx
$20000\int_{-5}^{5}(\frac{1}{2+\lvert x\rvert}-\frac{e^{-2}}{2+\lvert x\rvert}$)dx
$20000*(1-e^{-2})\int_{-5}^{5}\frac{dx}{2+\lvert x\rvert}$
$20000*(1-e^{-2})(\int_{-5}^{0}\frac{dx}{2-x}+\int_{0}^{5}\frac{dx}{2+x}$
$20000*(1-e^{-2})(-ln(2)+ln(2-(-5))+ln(2+5)-ln2)$
$20000*(1-e^{-2})*2(ln7-ln2)$
$40000*(1-e^{-2})*ln(7/2)\approx43,329$
