Chapter 5.5, Problem 92E

Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is

$\frac{dx}{dt}=5000\left(1-\frac{100}{{(t+10)}^2}\right)\text{calculators}/\text{week}$

(Notice that production approaches 5000 per week as time goes on, but the initial production is lower because of the workers’ unfamiliarity with the new techniques.) Find the number of calculators produced from the beginning of the third week to the end of the fourth week.