3. The function r(t) graphed below gives the rate at which water is flowing into or out of a backyard swimming pool one afternoon. (Positive rates mean water is flowing into the pool.) Time t is measured in hours since noon, and the rate r(t) is measured in gallons per hour. At 1 pm, there are 500 gallons of water in the pool. r(t) 180- 120 60 2 3 -60 -120- -180 -240- (a) Write an expression involving a definite integral that gives the exact amount of water in the pool at 3 pm. (b) Write an expression involving a definite integral that gives the exact amount of water in the pool at 2 pm, and then evaluate this expression exactly. (c) Is water flowing into or out of the pool between 1 pm and 2 pm? Based on that, should there be more water in the pool at 1 pm or at 2 pm? Make sure your answer to (b) is consistent with this. (Remember that we are told there are 500 gallons of water in the pool at 1 pm.) (d) Write an expression involving a definite integral that gives the exact amount of water in the pool x hours after noon