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# Answer: Temperature data Hourly temperature data for ## Problem 29E Chapter 7.6

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:
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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 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 = =...

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