During a 4-hour storm, the instantaneous rainfall rate (in inches per hour) R is modeled for 0≤t≤4 by
R(t)=0.015t2+0.20t+1.00,
where t is measured in hours since the storm began.
a. Calculate the average rainfall rate during the storm.
b. Determine the total depth of rain that fell during the 4-hour period by using the average rate from part (a). Then verify that this result equals the value of ∫04R(t)dt.