Use definite integral with traffic rate function to determine total number of cars

In this calculus example, we work on a word problem that involves a rate of traffic flow function being given to us and we are tasked with finding the total number of cars that go through an intersection in a given time interval. We use a definite integral and the power rule of integration to accomplish this task.

The traffic flow rate (cars per hour) across an intersection is a quadratic function where t is in hours, and t=0 is 6am. How many cars pass through the intersection between 6am and 10am?