524
Chapter 5 | Integration
2 on [1, 2]
37. To help get in shape, Joe gets a new pair of running shoes. If Joe runs 1 mi each day in week 1 and adds 1 10 mi to his daily routine each week, what is the total mileage on Joe’s shoes after 25 weeks? 38. The following table gives approximate values of the average annual atmospheric rate of increase in carbon dioxide (CO 2 ) each decade since 1960, in parts per million (ppm). Estimate the total increase in atmospheric CO 2 between 1964 and 2013. Decade Ppm/y
24. L 30 for f ( x ) = x
2 on [−2, 2]
25. L 10 for f ( x ) = 4− x
26. R 20 for f ( x ) = sin x on [0, π ] 27. R 100 for ln x on [1, e ]
In the following exercises, graph the function then use a calculator or a computer program to evaluate the following left and right endpoint sums. Is the area under the curve on the given interval better approximated by the left Riemann sum or right Riemann sum? If the two agree, say "neither." 28. [T] L 100 and R 100 for y = x 2 −3 x +1 on the interval [−1, 1]
1964–1973 1.07
1974–1983 1.34
2 on the interval [0, 1]
1984–1993 1.40
29. [T] L 100 and R 100 for y = x
x +1 x 2 −1
on the interval [2, 4]
30. [T] L 50 and R 50 for y =
1994–2003 1.87
2004–2013 2.07
3 on the interval [−1, 1]
31. [T] L 100 and R 100 for y = x
Table 5.2 Average Annual Atmospheric CO 2 Increase, 1964–2013 Source : http://www.esrl.noaa.gov/ gmd/ccgg/trends/.
32. [T] L 50 and R 50 for y = tan( x ) on the interval ⎡ ⎣ 0, π 4
⎤ ⎦
2 x on the interval [−1, 1]
33. [T] L 100 and R 100 for y = e
34. Let t j denote the time that it took Tejay van Garteren to ride the j th stage of the Tour de France in 2014. If there were a total of 21 stages, interpret ∑ j =1 21 t j . 35. Let r j denote the total rainfall in Portland on the j th day of the year in 2009. Interpret ∑ j =1 31 r j . 36. Let d j denote the hours of daylight and δ j denote the increase in the hours of daylight from day j −1 to day j in Fargo, North Dakota, on the j th day of the year. Interpret d 1 + ∑ j =2 365 δ j .
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online