This problem is similar to Probem 6 on the Final Exam Study Guide. In that problem and the one below, you are given a derivative and asked to undo the derivative with an antiderivative.

Problem 8 Suppose a company spends R million dollars on research annually. The rate S ’(R) at which sale are increasing at a company is given by

If the annual research budget is increased from 3 million dollars to 4 million dollars, how much will sales increase?

Solution To find the change in sales from R = 3 to R = 4 using the derivative of sales, we need to compute a definite integral:

Since the rate was in dollars of sales per dollars of research, area under the curve has units of

This means the increase in sales was 50.1875 million dollars.