The rate at which water flows through Table Rock Dam on the White Rive in Branson, MO, is measured in thousands of cubic feet per second (TCFS). As engineers open

the floodgates, flow rates are recorded according to the following chart.' 1. What question might the engineers be interested in answering using this data? Why would it be easier to measure flow rate instead of directly what they want to measure? 2. What definite integral describes what the engineers are trying to measure about the dam in the 60-second time period? 3. Graph the data. 4. Think about the situation that is being measured, if you were to connect the data points would it be smooth curves or straight lines? Why? 5. Use the data to calculate Mn for the largest possible n to approximate what you are trying to measure in (2). Do you think Mn over- or under-estimates the exact value of the integral?Why? 6. Approximate the integral in (2) by calculating Sn for the largest possible n. 2000+2100+2400+3000+3900+5100+6500Compute S, and60What7quantity do both of these values estimate? Which is a moreaccurate approximation?