Chapter 8.3, Problem 37E

Seasonal business cycle. Suppose that profits on the sale of swimming suits in a department store are given approximately by

$P\left(t\right)=5-5\cos \frac{\pi t}{26}0\le t\le 104$

where P(t) is profit (in hundreds of dollars) for a week of sales t weeks after January 1. Use definite integrals to approximate

(A)    The total profit earned during the 2-year period

(B)    The total profit earned from t = 13 to t = 26

(C)    Illustrate part (B) graphically with an appropriate shaded region representing the total profit earned.