The density of people (number of people per mile) during the evening rush hour for the 5 mile stretch along a certain sidewalk i
n New York is given by f(x), where x is the distance in miles north of the subway station. Which of the following gives the number of people on this 5 mile stretch from the subway? 5
a. ∫ f(x). dx
0
Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:
