×
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 23e
Get Full Access to Calculus: Early Transcendentals - 1 Edition - Chapter 7.6 - Problem 23e

×

# Comparing the Midpoint and Trapezoid Rules pply the

ISBN: 9780321570567 2

## Solution for problem 23E Chapter 7.6

Calculus: Early Transcendentals | 1st Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Calculus: Early Transcendentals | 1st Edition

4 5 1 305 Reviews
28
5
Problem 23E

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

===0.0976

Step7

Using midpoint rule

0.024544

Midpoint sum for N=32

++-------+)

++-------+)

=1.4266

Error for N=32 for midpoint rule

==0.048918

Step8

Table for midpoint approximation and error

 N Approximation Error 4 0.93193 0.37871 8 1.2093 0.19379 16 1.3536 0.0976 32 1.4266 0.048918

Step9

N=4

Using trapezoidal rule

0.19635

Trapezoidal  sum for N=4

=1.4952

Error for N=4 for Trapezoidal  rule

==0.012884204

Step10

N=8

Using trapezoidal rule

Trapezoidal  sum for N=8

=1.4952

Error for N=8 for Trapezoidal  rule

==0.0032148

Step11

N=16

Using trapezoidal rule

Trapezoidal  sum for N=16

=1.4988

Error for N=16 for Trapezoidal  rule

==0.00080332

Step12

N=32

Step 2 of 3

Step 3 of 3

#### Related chapters

Unlock Textbook Solution