   Chapter 6.3, Problem 4E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Using the Trapezoidal Rule and Simpson’s Rule In Exercises 1-10, use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of the definite integral. Round your answers to four decimal places. See Examples 1 and 2. ∫ 1 2 2 x d x , n = 8

To determine

The value of the integral 122xdx,n=8 by using the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of definite integral. Round your answers to four decimal places.

Explanation

Given Information:

The definite integral is 122xdx,n=8.

Formula used:

1. Trapezoidal Rule:

If a function f is continuous on [a,b], then

abf(x)dx(ba2n)[f(x0)+2f(x0)+...+2f(xn1)+f(xn)]

2. Simpson’s Rule:

If f is continuous on [a,b] and n is an even integer, then

abf(x)dx(ba3n)[f(x0)+4f(x1)+2f(x2)+4f(x3)++4f(xn1)+f(xn)]

Calculation:

Calculation to get exact value:

Consider the definite integral 122xdx,n=8.

122xdx=2ln|x|12=2ln21.3863

Therefore, the exact value: 122xdx1.3863.

Calculation by Trapezoidal Rule:

Consider the definite integral 122xdx,n=8.

When n=8, the width of each subinterval is.

218=18

And the end points of subintervals are.

For x0,

x0=1

For x1,

x1=98

For x2,

x2=54

For x3,

x3=54+18=118

For x4,

x4=118+18=128=32

For x5,

x5=32+18=138

For x6,

x6=138+18=74

For x7,

x7=74+18=158

For x8,

x8=158+18=2

By Trapezoidal Rule,

122xdx=12×8

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Differentiate the function. S(p)=pp

Single Variable Calculus: Early Transcendentals, Volume I

#### In Exercises 73-80, find the indicated limits, if they exist. 74. limx4x21x+2

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### In problems 37-48, compute and simplify so that only positive exponents remain. 42.

Mathematical Applications for the Management, Life, and Social Sciences 