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# Comparing the Midpoint and Trapezoid Rules pply the ## Problem 23E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

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Problem 23E

Comparing the Midpoint and Trapezoid Rules

pply the Midpoint and Trapezoid Rules to the following integrals. Make a table similar to Table 7.4 showing the approximations and errors for n = 4,8, 16, and 32. The exact values of the integrals are given for computing the error. Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

Apply the Midpoint and Trapezoid Rules to the following integrals.

n = 4,8, 16, and 32

The exact values of the integrals are given for computing the error. Step2

To find

Make a table  showing the approximations and errors for n = 4,8, 16, and 32.

Step3

a=0 , b= 0.7854, (N=4,8,16,32)

Using midpoint rule Step4

Midpoint sum for N=4  + +-------+ )  + +-------+ ) =0.93193

Error for N=4 for midpoint rule = = =0.37871

Step5

Using midpoint rule Midpoint sum for N=8  + +-------+ )  + +-------+ ) =1.2093

Error for N=8 for midpoint rule = = =0.19379

Step6

Using midpoint rule  Midpoint sum for N=16  + +-------+ )  + +-------+ ) =1.3536

Error for N=16 for midpoint rule = =

Step 2 of 3

Step 3 of 3

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