Chapter 12.2, Problem 50E

Production The rate of production of a new line of products is given by

$\frac{dx}{dt}=200\left[1+\frac{400}{{\left(t+40\right)}^2}\right]$ where x is the number of items and t is the number of weeks the product has been in production.

(a) Assuming that $x=0$ when $t=0$, find the total number of items produced as a function of time t.

(b) How many items were produced in the fifth week?