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Definite Integrals and Rate of Change

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16. An old rowboat has sprung a leak. Water is flowing into the boat at a rate given in the following table.

t minutes 0 5 10 15
r(t), liters/min 12 20 24 16

(a) Compute upper and lower estimates for the volume of water that has flowed into the boat during the 15 minutes.
Number of subintervals: ?????
Width of each subinterval: ?????

Interval Minimum Endpoint Maximum Endpoint

Lower Estimate: ????

Upper Estimate: ????

(b) Draw a graph to illustrate the lower estimate. (Once you have the graph completed, you can use the Drawing Toolbar to create appropriate rectangles.)

Insert your graph.

30, 31
30. Use a graph of to explain why must be between 0 and 2.
(Try x values from -1 to 1 with major units of 0.2 and y values from 0 to 1.2 with major units of 0.2.)
Insert your graph.

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Definite Integrals and Rate of Change are investigated. The solution is detailed and well presented.

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16. An old rowboat has sprung a leak. Water is flowing into the boat at a rate given in the following table.

t minutes 0 5 10 15
r(t), liters/min 12 20 24 16

(a) Compute upper and lower estimates for the volume of water that has flowed into the boat during the 15 minutes.
Number of subintervals: 3
Width of each subinterval: 5

Interval Minimum Endpoint Maximum Endpoint
(0, 5) 60 100
(5, 10) 100 120
(10, 15) 80 120

Lower Estimate: 240

Upper ...

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