The density of people (number of people per mile) during the evening rush hour for the 5-mile stretch along a certain sidewalk in 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?
a) integral from 0 to 5
b) integral from 0 to x
c) integral from 5 to x
d) integral from x to 5
integral of number/mile dx from x = 0 to x = 5
.... sketch it
The correct answer is option a) integral from 0 to 5.
When calculating the number of people on the 5-mile stretch from the subway, you need to integrate the density function f(x) over the entire 5-mile interval. Integrating from 0 to 5 encompasses the entire stretch, resulting in the total number of people along the sidewalk.
Therefore, the integral from 0 to 5 is the correct choice to calculate the number of people on the 5-mile stretch from the subway.
To find the number of people on the 5-mile stretch from the subway, we need to calculate the integral of the density function f(x) over the entire 5-mile distance.
The correct option is:
a) integral from 0 to 5
This is because the integral from 0 to 5 represents the total accumulation of the density function f(x) over the entire 5-mile stretch. Integrating from 0 to 5 will calculate the total number of people on the sidewalk from the subway station to the end of the 5-mile stretch.
Options b), c), and d) involve integrating from specific points (0 or 5) to a variable x. These options would give partial accumulations of the density function, and not the total number of people on the entire 5-mile stretch.