Chapter 8.5, Problem 62E

Water Supply The flow rate R (in thousands of gallons per hour) of water at a pumping station during a day can be modeled by

$R=53+7\sin \left(\frac{\pi t}{6}+3.6\right)+9\cos \left(\frac{\pi t}{12}+8.9\right)$,

$0\le t\le 24$ where t is the time (in hours), with t = 0 corresponding to midnight.

Find the average hourly flow rate from midnight to noon $\left(0\le t\le 12\right)$.

Find the average hourly flow rate from noon to midnight $\left(12\le t\le 24\right)$.

Find the total volume of water pumped in one day.