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Answer: Temperature data Hourly temperature data for

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Problem 29E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 29E

Temperature data Hourly temperature data for Boulder, CO, San Francisco, CA, Nantucket, MA, and Duluth, MN, over a 12-hr period on the same day of January are shown in the figure. Assume that these data are taken from a continuous temperature function T(t). The average temperature over the 12-hr period is .

Find an accurate approximation to the average temperature over the 12-hr period for Nantucket. State your method.

Step-by-Step Solution:
Step 1 of 3

Problem 29E

Temperature data Hourly temperature data for Boulder, CO, San Francisco, CA, Nantucket, MA, and Duluth, MN, over a 12-hr period on the same day of January are shown in the figure. Assume that these data are taken from a continuous temperature function T(t). The averagetemperature over the 12-hr period is .

Find an accurate approximation to the average temperature over the 12-hr period for Nantucket. State your method.

Answer;

    Step-1;

               Given that temperature  data  hourly temperature data for Boulder  , Co,San francisco ,CA, Nantucket ,MA , and Duluth ,MN  over a 12 -hr  period on the same day of  January  are shown  in the figure.

                             

  And also given that these data  from a continuous   temperature function T(t) .The average temperature over the 12-hr period is   = T(t) dt.

Given table is ;

Step-2 ;

        Now , we have to find out an accurate approximation to the average temperature over the 12-hr period  for Nantucket.

           For our convenience in this problem we have to choose midpoint  Rule approximations  to the given integral.

            Midpoint  sum (also Midpoint approximation  )  uses midpoint of subintervals;

                     f(x) dx   (f() + f() +f() +.............+f()+f())

                                      Where  =  , a =  and b = , [a ,b] is the interval .

              [ ] ,  [ ]  ,   [ ] ………..  [ ]  are the subintervals in   [ a , b]  .

Step-3;

          Now , the given integral is ;    = T(t) dt.

          Now, we have to indicated midpoint Rule approximations  to the given integral ,using n = 6 subintervals.

                      n= 6  , a =   = 0 and b = = 12  , then   =  =  = 2.

                   Divide interval [0, 12]  into  n =6 , subintervals of length  = 2  with the following endpoints a =  =...

Step 2 of 3

Chapter 7.6, Problem 29E is Solved
Step 3 of 3

Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

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