Chapter 8.3, Problem 38E

Seasonal business cycle. Revenues from sales of a soft drink over a 2-year period are given approximately by

$R\left(t\right)=4-3\cos \frac{\pi t}{6}0\le t\le 24$

where R(t) is revenue (in millions of dollars) for a month of sales t weeks after February 1. Use definite integrals to approximate

(A)    Total revenues taken in over the 2-year period

(B)    Total revenues taken in from t = 8 to t = 14

(C)    Illustrate part (B) graphically with an appropriate shaded region representing the total revenues taken in.