   Chapter 6.3, Problem 19E ### 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 11-20, approximate the value of the definite integral using (a) the Trapezoidal Rule and (b) Simpson's Rule for the indicated value of n. Round your answers to three decimal places. See Examples 1 and 2. ∫ 0 3 1 2 − 2 x + x 2 d x , n = 6

(a)

To determine

To calculation: The value of the integral 03122x+x2dx,n=6 by using the Trapezoidal Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

Explanation

Given Information:

The definite integral is 03122x+x2dx,n=6.

Formula used:

Trapezoidal Rule:

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

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

Calculation:

Consider the definite integral 03122x+x2dx,n=6.

When n=6, the width of each subinterval is

306=36=12

And the end points of subintervals are

x0=0x1=12x2=1x3=32

And,

x4=2x5=52x6=3

Thus, the graph of the function for interval,

(b)

To determine

To calculation: The value of the integral 03122x+x2dx,n=6 by using the Simpson’s Rule and to approximate the value of the definite integral for the indicated value of n. Round your answers to four decimal places.

### 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

#### Sketch the region in the xy-plane. 45. {(x, y) | xy 0}

Single Variable Calculus: Early Transcendentals, Volume I

#### What is the value of (X + 1) for the following scores: 0, 1, 4, 2? a. 8 b. 9 c. 11 d. 16

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

#### In Exercises 13-20, sketch a set of coordinate axes and plot each point. 20. (1.2, 3.4)

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