The rate at which rainwater flows into a drain pipe is modeled by the function r, where r of t is equal to 20 sin of t squared over 35 cubic feet per hour. t is measured in hours, and 0 is less than or equal to t, which is less than or equal to 8, so t is going to go between 0 and 8. The pipe is partially blocked, allowing water to drain out the other end of the pipe at a rate modeled by d of t. It's equal to negative 0.04 t to the third power, plus 0.4 t squared plus 0.96 t cubic feet per hour. For the same interval, right over here, there are 30 cubic feet of water in the pipe at time t equals 0. Part a. How many cubic feet of rainwater flow into the pipe during the 8 hour time interval 0 is less than or equal to t is less than or equal to 8? Alright, so we know the rate, the rate that things flow into the rainwater pipe.