Use a trapezoidal sum with the four sub-intervals indicated by the data in the table to estimate the definite integral from 0 to 8 of R of t, dt. Using correct units, explain the meaning of your answer in terms of water flow. Give 3 decimal places in your answer.

t(hours) 0 | 2 | 3 | 7 | 8
R(t) (gallons per hour) 1.95 | 2.5 | 2.8 | 4 | 4.26

Answers

    The area of a trapezoid is given by . If we take the height to be the change in x, then  is the area of one trapezoid for one subinterval with borders and . Therefore, we approximate as follows, using the data to dictate our trapezoid bases and heights:     From t = 0 hours to t = 8 hours, the total amount of water that flows out is approximately 24.83 gallons.


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