Use an integral to calculate the population in the whole town of Squaresburg. Round your answer to the nearest whole number (if appropriate). Population in the whole town ≈ people
The city of Squaresburg is in the shape of a rectangle, whose border is shown in the graph below. A highway running along the x-axis borders one side of the town, and the grid is shown in miles along each axis.
The population density of Squaresburg is a(y)=2000-500y, where a(y) is measured in peoplemile2 and y is measured in miles from the highway.
Consider a thin, rectangular slice of the town, cut parallel to the x-axis with thickness Δy. Write an expression that approximates the population living in this region.
Population in this region ≈ Δy
Use an integral to calculate the population in the whole town of Squaresburg. Round your answer to the nearest whole number (if appropriate).
Population in the whole town ≈ people
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