Answer
$\approx 43328$
Work Step by Step
Our aim is to integrate the integral as follows:
$\int ^5_{-5} \int ^0_{-2} \dfrac{10,000e^y}{1+\dfrac{|x|}{2}} \space dy \space dx $
or, $=10,000 \times \int ^5_{-5}\dfrac{1-e^{-2} dx}{1+\dfrac{|x|}{2}})$
or, =$10000 \times (1-e^{-2})[\int^0_{-5}\dfrac{dx}{1-\dfrac{x}{2}}+\int ^5_0 \dfrac{1}{1+\dfrac{x}{2}} dx $
or, $=10000 \times (1-e^{-2})[- 2 \ln(1-\dfrac{x}{2})]^0_{-5}+10000 \times (1-e^{-2})[2 \ln(1+\dfrac{x}{2})]^5_0$
or, $=10,000(1-e^{-2})[2 \ln(1+\dfrac{5}{2})]+10,000(1-e^{-2})[2ln(1+\dfrac{5}{2})]$
or, $=40,000(1-e^{-2}) \ln(\dfrac{7}{2}) \approx 43328$
