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# Midpoint Rule approximations Find the indicated Midpoint ISBN: 9780321570567 2

## Solution for problem 11E Chapter 7.6

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

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

Step 3 of 3

##### 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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