Textbook Problem

Population Density The population density (in people per square mile) for a coastal town on an island can be modeled by

$f\left(x,y\right)=\frac{5000x{e}^y}{1+2x^2}$ where x and y are measured in miles. What is the population inside the rectangular area defined by the vertices (0, 0), (4, 0), (0, −2), and (4, −2)? Is the average population density of the town more than 500 people?