   Chapter 8, Problem 45RE

Chapter
Section
Textbook Problem

Using the Trapezoidal Rule and Simpson's Rule In Exercises 45–48, approximate the definite integral using the Trapezoidal Rule and Simpson’s Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. ∫ 2 3 2 1 + x 2 d x

To determine

To calculate: The approximate area of the integral 2321+x2dx using Trapezoidal and Simpson’s Rule.

Explanation

Given:

The provided integral is

2321+x2dx

And number of subintervals to be used n=4

Formula used:

If f(x) is continuous on [a,b] then Trapezoidal rule for approximating abf(x)dx is

abf(x)dxba2n[f(x0)+2f(x1)+2f(x2)++2f(xn1)+f(xn)]

Where n is be an even integer and is called number of subintervals.

And

Simpson’s Rule for approximating abf(x)dx is

abf(x)dxba3n[f(x0)+4f(x1)+2f(x2)+4f(x3)+2f(xn2)+4f(xn1)+f(xn)]

Calculation:

When n=4, then the width of each subinterval Δx=ba4. For the provided integral a=2 and

b=3.

So,

Δx=324=14

And the provided function is f(x)=2x2+1

Now apply Trapezoidal rule. That is,

abf(x)dxba2n[f(x0)+2f(x1)+2f(x2)++2f(xn1)+f(xn)]

Put values of f(x),a and b

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

Find more solutions based on key concepts 