BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Solutions

Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
Textbook Problem

Use Simpson’s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by a calculator.

26. y = x 3 , 1 ≤ x ≤ 6

To determine

To find: The arc length of the curve.

Explanation

Given information:

The curve function is y=x3 (1)

The lower limit is a=1 and the upper limit is b=6.

The number of intervals is 10.

Calculation:

The Simpson’s rule is shown below:

abf(x)dxSn=Δx3[f(x0)+4f(x1)+2f(x2)+4f(x3)+...+2f(xn2)+4f(xn1)+f(xn)] (2)

The interval width Δx=ban (3)

Here, the value of the function f(x) at x=0ton is f(x0)tof(xn), the upper limit is b, the lower limit is a, and the number of interval is n.

Find the value of f(x) using the relation:

f(x)=1+(dydx)2 (4)

Here, the derivative of the function y is dydx.

Differentiate Equation (1) with respect to x.

dydx=13x23

Substitute 13x23 for dydx in Equation (4).

f(x)=1+(13x23)2=1+19x43 (5)

Find the width of the interval:

Substitute 6 for b, 1 for a, and 10 for n in Equation (3).

Δx=6110=12

Modify Simpson’s rule for n=10.

S10=Δx3[f(x0)+4f(x1)+2f(x2)+4f(x3)+...+2f(x8)+4f(x9)+f(x10)] (6)

Split the interval 1 to 6 into 10 subintervals. Thus the intervals are 1,1.5,2,2.5,3,3.5,4,4.5,5,5.5,and6.

Substitute 1 for x0, 1.5 for x1, 2 for x2, 2.5 for x3, 3 for x4, 3

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
Sect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.2 P-1ESect-8.2 P-2ESect-8.2 P-3ESect-8.2 P-4ESect-8.2 P-5ESect-8.2 P-6ESect-8.2 P-7ESect-8.2 P-8ESect-8.2 P-9ESect-8.2 P-10ESect-8.2 P-11ESect-8.2 P-12ESect-8.2 P-13ESect-8.2 P-14ESect-8.2 P-15ESect-8.2 P-16ESect-8.2 P-17ESect-8.2 P-18ESect-8.2 P-19ESect-8.2 P-20ESect-8.2 P-21ESect-8.2 P-22ESect-8.2 P-23ESect-8.2 P-24ESect-8.2 P-27ESect-8.2 P-28ESect-8.2 P-29ESect-8.2 P-30ESect-8.2 P-31ESect-8.2 P-32ESect-8.2 P-33ESect-8.2 P-35ESect-8.2 P-36ESect-8.2 P-37ESect-8.2 P-38ESect-8.2 P-39ESect-8.3 P-1ESect-8.3 P-2ESect-8.3 P-3ESect-8.3 P-4ESect-8.3 P-5ESect-8.3 P-6ESect-8.3 P-7ESect-8.3 P-8ESect-8.3 P-9ESect-8.3 P-10ESect-8.3 P-11ESect-8.3 P-12ESect-8.3 P-13ESect-8.3 P-14ESect-8.3 P-15ESect-8.3 P-16ESect-8.3 P-17ESect-8.3 P-18ESect-8.3 P-19ESect-8.3 P-20ESect-8.3 P-21ESect-8.3 P-22ESect-8.3 P-23ESect-8.3 P-24ESect-8.3 P-25ESect-8.3 P-26ESect-8.3 P-27ESect-8.3 P-28ESect-8.3 P-29ESect-8.3 P-30ESect-8.3 P-31ESect-8.3 P-32ESect-8.3 P-33ESect-8.3 P-34ESect-8.3 P-35ESect-8.3 P-36ESect-8.3 P-37ESect-8.3 P-38ESect-8.3 P-39ESect-8.3 P-40ESect-8.3 P-41ESect-8.3 P-42ESect-8.3 P-43ESect-8.3 P-44ESect-8.3 P-45ESect-8.3 P-46ESect-8.3 P-47ESect-8.3 P-48ESect-8.3 P-49ESect-8.3 P-50ESect-8.3 P-51ESect-8.4 P-1ESect-8.4 P-2ESect-8.4 P-3ESect-8.4 P-4ESect-8.4 P-5ESect-8.4 P-6ESect-8.4 P-7ESect-8.4 P-8ESect-8.4 P-9ESect-8.4 P-10ESect-8.4 P-11ESect-8.4 P-12ESect-8.4 P-13ESect-8.4 P-14ESect-8.4 P-15ESect-8.4 P-16ESect-8.4 P-17ESect-8.4 P-18ESect-8.4 P-19ESect-8.4 P-20ESect-8.4 P-21ESect-8.4 P-22ESect-8.4 P-23ESect-8.5 P-1ESect-8.5 P-2ESect-8.5 P-3ESect-8.5 P-4ESect-8.5 P-5ESect-8.5 P-6ESect-8.5 P-7ESect-8.5 P-8ESect-8.5 P-9ESect-8.5 P-10ESect-8.5 P-11ESect-8.5 P-12ESect-8.5 P-13ESect-8.5 P-14ESect-8.5 P-15ESect-8.5 P-16ESect-8.5 P-17ESect-8.5 P-18ESect-8.5 P-19ESect-8.5 P-20ESect-8.5 P-21ECh-8 P-1RCCCh-8 P-2RCCCh-8 P-3RCCCh-8 P-4RCCCh-8 P-5RCCCh-8 P-6RCCCh-8 P-7RCCCh-8 P-8RCCCh-8 P-9RCCCh-8 P-10RCCCh-8 P-1RECh-8 P-2RECh-8 P-3RECh-8 P-4RECh-8 P-5RECh-8 P-6RECh-8 P-7RECh-8 P-8RECh-8 P-9RECh-8 P-10RECh-8 P-11RECh-8 P-12RECh-8 P-13RECh-8 P-14RECh-8 P-15RECh-8 P-16RECh-8 P-17RECh-8 P-18RECh-8 P-19RECh-8 P-20RECh-8 P-21RECh-8 P-22RECh-8 P-23RECh-8 P-1PCh-8 P-2PCh-8 P-3PCh-8 P-4PCh-8 P-5PCh-8 P-6PCh-8 P-7PCh-8 P-8PCh-8 P-9PCh-8 P-10PCh-8 P-11PCh-8 P-12PCh-8 P-13P

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

In Exercises 1728, use the logarithm identities to obtain the missing quantity.

Finite Mathematics and Applied Calculus (MindTap Course List)

Find the sum of the series. 1e+e22!e33!+e44!

Calculus (MindTap Course List)

In Exercises 99-106, factor out the greatest common factor from each expression. 99. 4x5 2x4 6x3

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

Perform the indicated operation for the following. 2.

Contemporary Mathematics for Business & Consumers

In RSTV, VT=3x1,TS=2x+1,andRS=4(x2). Find the value of x._

Elementary Geometry for College Students

What is the integrating factor for xy′ + 6x2y = 10 − x3?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th