A city along the edge of a river is semi-circular shaped with a radius 16 miles. In each case below, determine the shape of the strip that would be appropriate for the given population density. Then write a definite integral to represent the total population in the city.

(a) The population density is p(x) = -20x + 500 people per square mile where x is the distance in miles from the center of the city.

(b) The population density is p(x) = 175 people per square mile where x is the vertical distance in miles from the river.