Chapter 5 | Integration
581
247. [T] The graph below plots the cubic p ( t ) =0.07 t 3 +2.42 t 2 −25.63 t +521.23 against the data in the preceding table, normalized so that t =0 corresponds to 1963. Estimate the average number of bald eagles per year present for the 37 years by computing the average value of p over [0, 37].
Population of Breeding Pairs of Bald Eagles
Year
1963 487
1974 791
1981 1188
1986 1875
1992 3749
1996 5094
2000 6471
248. [T] Suppose you go on a road trip and record your speed at every half hour, as compiled in the following table. The best quadratic fit to the data is q ( t ) =5 x 2 −11 x +49, shown in the accompanying graph. Integrate q to estimate the total distance driven over the 3 hours. Time (hr) Speed (mph)
Table 5.11 Population of Breeding Bald Eagle Pairs Source : http://www.fws.gov/Midwest/eagle/ population/chtofprs.html.
246. [T] The graph below plots the quadratic p ( t ) =6.48 t 2 −80.31 t +585.69 against the data in preceding table, normalized so that t =0 corresponds to 1963. Estimate the average number of bald eagles per year present for the 37 years by computing the average value of p over [0, 37].
0 (start)
50
1
40
2
50
3
60
As a car accelerates, it does not accelerate at a constant rate; rather, the acceleration is variable. For the following exercises, use the following table, which contains the acceleration measured at every second as a driver merges onto a freeway.
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