Bob leaves for a trip at 3pm (time t = 0) and drives with velocity miles per hour, where t is measured in hours. Find
and explain what it represents in the language of the problem.
First we find the value of the integral:
To explain what the integral represents in the language of the problem, we need to know units for t and units for the integral. We're told that t is measured in hours and v(t) in miles per hour. This means the integral is measured in miles. So
is the distance Bob drove from time t = 0 hours to time t = 2 hours. Since we're told 3pm corresponds to t = 0, t = 2 corresponds to 5pm. Putting everything together,