(1) A reservoir of water has a source owing in, and water is draining out as well, so that the volume of water in the reservoir is changing over time. Suppose f (t) is the rate of change of the volume of water in the reservoir, measured in gallons/ hour. Here is the graph of f (t): y = f(t) (gallons/ hour) > 13 (hours) The part of the graph of f on the interval [2, 0] is a quarter circle of radius 2 centered at (0, O). t is measured in hours. t = 0 corresponds to noon, so that the graph gives information about the rate of change of water between 10am (t = 2) and 4pm (t = 4). 4 (a) Evaluate / f(t) dt. Show your method clearly. 2 (b) Is there more water in the reservoir at 10am (t = 2) or at 4pm (t = 4)? Explain your reasoning. ((3) Suppose there are 1000 gallons of water in the reservoir at 10am (t = 2). How many gallons of water are there at 4pm (t = 4)