Chapter 6.1, Problem 39E

Oil production An oil refinery produces oil at a variable rate given by

$Q^{\prime }(t)=\{\begin{array}{ll}800\hfill & \text{if}0\le t<30\hfill \\ 2600-60t\hfill & \text{if}30\le t<40\hfill \\ 200\hfill & \text{if}t\ge 40,\hfill \end{array}$

where t is measured in days and Q is measured in barrels.

1. a. How many barrels are produced in the first 35 days?
2. b. How many barrels are produced in the first 50 days?
3. c. Without using integration, determine the number of barrels produced over the interval [60, 80].