he population density (in people per square kilometer) in a rural town is a func
ID: 2893418 • Letter: H
Question
he population density (in people per square kilometer) in a rural town is a function p(r)p(r) of distance rr (in kilometers) from the center of this town --- the following table has some values of this population density function.
Population Density
Estimate the total population within 1.2 kilometers of this town's center by averaging the left- and right-endpoint approximations of an appropriate definite integral.
Total population (within 1.2 km) is approximately
rr 0 0.2 0.4 0.6 0.8 1 1.2 p(r)p(r) 127 103.2 81.8 69.4 53.8 45.1 37.3Explanation / Answer
here x = 0.2
Left endpoint approximation L = p(0) * x + p(0.2) * x + p(0.4) * x + p(0.6) * x + p(0.8) * x + p(1) * x
==> L = 127 * (0.2) + 103.2 * (0.2) + 81.8 * (0.2) + 69.4 * (0.2) + 53.8 * (0.2) + 45.1 * (0.2)
==> L = 96.06
Right endpoint approximation R = p(0.2) * x + p(0.4) * x + p(0.6) * x + p(0.8) * x + p(1) * x + p(1.2) * x
==> R = 103.2 * (0.2) + 81.8 * (0.2) + 69.4 * (0.2) + 53.8 * (0.2) + 45.1 * (0.2) + 37.3 * (0.2)
==> R = 78.12
Average = (L + R)/2 = (96.06 + 78.12)/2 = 87.09
Hence approximate population within 1.2 km = 87.09
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