The Original Produce Rate

Substitution Function for the
Produce Rate Function

Lansing automobile company is manufacturing a new model of car with a produce rate of

How many cars can be produced in the first season?

The output of the car is the integral of the production rate with respect to time in the range between 0 and 3 months.

Let u = t + 20. The derivative of u with respect to time t is

     du/dt = 1

Rearrange the above equation gives

     du = dt

The new limits of integration can be calculated. When t = 0, u = 20 and when t = 3, u = 23. The substitution rule gives that

Thererfore,