The ∫f(x)dx represents the total number of people on the 5-mile stretch from the subway station, based on the density function f(x). The correct answer is ∫f(x)dx.
This integral represents the total number of people (N) on the 5-mile stretch along the sidewalk from the subway station.
The density function f(x) gives the number of people per mile at any given point x along the sidewalk. To determine the total number of people, we need to sum up the density at each point along the 5-mile stretch. This is where the integral comes in.
The integral symbol ∫ represents summation over a continuous interval. The function f(x) is being integrated from x = 0 (the subway station) to x = 5 (the end of the 5-mile stretch). This means we are summing up the density f(x) at each point along the 5-mile stretch, giving us the total number of people N.
Therefore, ∫f(x)dx represents the total number of people on the 5-mile stretch from the subway station, based on the density function f(x).