Chapter 8.4, Problem 39E

Pollution. In a large city, the amount of sulfur dioxide pollutant released into the atmosphere due to the burning of coal and oil for heating purposes is given approximately by

$P\left(n\right)=1+\cos \frac{\pi n}{26}0\le n\le 104$

where P(n) is the amount of sulfur dioxide (in tons) released during the nth week after January 1.

(A)    How many tons of pollutants were emitted into the atmosphere over the 2-year period?

(B)    How many tons of pollutants were emitted into the atmosphere from n = 13 to n = 52?

(C)    Illustrate part (B) graphically with an appropriate shaded region representing the total tons of pollutants emitted into the atmosphere.