   Chapter 13.8, Problem 3CP ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# We can show that ∫ 0 2 4 x 3 d x =   16 . Use n = 4 subdivisions to find(a) the Trapezoidal Rule approximation of this integral.(b) the Simpsons Rule approximation of this integral.

(a)

To determine

To calculate: The approximate value of the integral 024x3dx where, n=4 using trapezoidal Rule.

Explanation

Given information:

The provided integral is,

024x3dx

Where, n=4

Formula used:

For each interval [a,b] and value of n,

h=ban

And,

xn=a+nh

According to trapezoidal rule,

abf(x)dxh2[f(x0)+2f(x1)+2f(x2)+2f(x3)f(xn)]

Calculation:

Consider the provided integral,

024x3dx

Where, n=4

And, a=0,b=2

For each interval [a,b] and value of n,

h=ban

And,

xn=a+nh

By using the above formula,

h=204=12

 i xi=a+ih f(xi)=4x3 0 0 0 1 0

(b)

To determine

To calculate: The approximate value of the integral 024x3dx;n=4 by using Simpson’s Rule.

### 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

#### Place the following set of n = 20 scores in a frequency distribution table.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

#### Solve the equations in Exercises 126. 2x3x12x+3x+1=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### How does a full-text database differ from other databases?

Research Methods for the Behavioral Sciences (MindTap Course List) 