Measurements are made of the rate at which water is draining from a container at various times, and recorded in the following table. t (min) 0.5 1 1.5 2 r(t) (liters/min) 17 16 14 10 2 (a) In a sentence or two, explain why someone would want to calculate r(t) dt. What is the meaning of this integral in the context of the problem? (b) Which of the left, right, midpoint, and trapezoid sums should you choose to produce the best approx- imation you can to the value of r(t) dt. Calculate the sum you selected, be sure to show enough work so that your method is clear. Provide a sentence to explain why you think this is the best approximation given the limitations of the table.

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