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Midpoint Rule approximations Find the indicated Midpoint

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 11E 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 11E

Midpoint Rule approximations

Find the indicated Midpoint Rule approximations to the following integrals.

 using n =1, 2, and 4 subintervals

Step-by-Step Solution:
Step 1 of 3

Problem 11E

Midpoint Rule approximations Find the indicated Midpoint Rule approximations to the following integrals.

 using n =1, 2, and 4 subintervals

Answer

Step-1;

             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-2

             

                     The given integral ;    2 dx.

         Now , we have to indicated midpoint Rule approximations  to the given integral  , using n = 1 , 2 and 4 subintervals.

                           Consider ; f(x) = 2  , a =   = 2 and b = = 10.

Step-3

                     n= 1  , a =   = 2 and b = = 10  , then   =  =  = 8.

                   Divide interval [2, 10]  into  n =1 , subintervals of length  = 8  with the following endpoints a =  = 2 , b =  =10.

          Now , we just evaluate function at those endpoints :  

                                   f( ) = f()   = f(6)

                     If x = 6 , then  f(x) = 2 

   

                                             f(6) = 2 = 72.

                   Therefore , the midpoint sum of n = 1 subintervals is ;

                 

                                                       2) dx   (f())

                                                                            (f (6))

                                               

                                                                             (72)   576.

                                                                         

                           

    Step-4

                     

                  n= 2  , a =   = 2 and b = = 10  , then   =  =  =  4.

                   Divide interval [2, 10]  into  n =2 , subintervals of length  = 4  with the following endpoints a =  = 2 , = 6 , and  b =  =10.

          Now , we just evaluate function at those endpoints :  

                                   f( ) = f()   = f(4)

                                   If x = 4 , then  f(x) = 2 

   

                                             f(4) = 2 =...

Step 2 of 3

Chapter 7.6, Problem 11E is Solved
Step 3 of 3

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

This full solution covers the following key subjects: approximations, rule, midpoint, Integrals, indicated. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 11E from 7.6 chapter was answered, more than 289 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The answer to “Midpoint Rule approximations Find the indicated Midpoint Rule approximations to the following integrals. using n =1, 2, and 4 subintervals” is broken down into a number of easy to follow steps, and 20 words. The full step-by-step solution to problem: 11E from chapter: 7.6 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.

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