Complete the table for n = 4, 8, 16, and 32 Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computingthe error.Complete the following table.(Type integers or decimals.)M(n)n(32²-23)(3x² - 2x) dx = 1004T(n)Absolute Errorin M(n)Absolute Errorin T(n)

Answered: Apply the Midpoint and Trapezoid Rules…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 74E

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Related questions

Question

Complete the table for n = 4, 8, 16, and 32

Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the approximations and errors for n = 4, 8, 16, and 32. The exact value of the integral is given for computing
the error.
Complete the following table.
(Type integers or decimals.)
M(n)
n
(32²-23)
(3x² - 2x) dx = 100
4
T(n)
Absolute Error
in M(n)
Absolute Error
in T(n)

Expert Solution

Step 1: Analysis and Introduction

Given Information:

$integral subscript 1 superscript 5 open parentheses 3 x squared minus 2 x close parentheses d x equals 100$ .

$n equals 4 comma 8 comma 16.32$ .

To find:

The approximate value of integration by midpoint rule and trapezoid rule.

Also, find the approximate error when compared to exact value.

Concept used:

Midpoint rule: $integral subscript a superscript b f open parentheses x close parentheses d x equals increment x sum from i equals 1 to n of f open parentheses top enclose x subscript i end enclose close parentheses$ , where $top enclose x subscript i end enclose$ is the midpoint of $i to the power of th$ sub-interval and $increment x equals fraction numerator b minus a over denominator n end fraction$ .

Trapezoidal rule: $integral subscript a superscript b f open parentheses x close parentheses d x equals fraction numerator increment x over denominator 2 end fraction open square brackets f open parentheses x subscript 0 close parentheses plus f open parentheses x subscript n close parentheses plus 2 open parentheses f open parentheses x subscript 1 close parentheses plus f open parentheses x subscript 2 close parentheses plus... plus f open parentheses x subscript n minus 1 end subscript close parentheses close parentheses close square brackets$