Explanation Given: The integral ∫ 1 2 ln x d x and n = 4 . Formula used: Trapezoidal Rule : ∫ a b f ( x ) d x ≈ Δ x 2 [ f ( x 0 ) + 2 f ( x 1 ) + ... + 2 f ( x n − 1 ) + f ( x n ) ] Where Δ x = b − a n and x n = a + n Δ x . Simpson’s Rule : ∫ a b f ( x ) d x ≈ Δ x 3 [ f ( x ) + 4 f ( x 1 ) + 2 f ( x 2 ) + ... + 4 f ( x n − 1 ) + f ( x n ) ] Where Δ x = b − a n and n is even. Calculation: Consider the integral ∫ 1 2 ln x d x . Here, a = 1 , b = 2 and n = 4 . Substitute a = 1 , b = 2 and n = 4 in Δ x = b − a n , Δ x = 2 − 1 4 = 1 4 The end point of the sub-intervals are x 0 = 1 , x 1 = 5 4 , x 2 = 3 2 , x 3 = 7 4 and x 4 = 2 . The Trapezoidal Rule yields, ∫ 1 2 ln x d x ≈ 1 4 2 [ f ( 1 ) + 2 f ( 5 4 ) + 2 f ( 3 2 ) + 2 f ( 7 4 ) + f ( 2 ) ] = 1 8 [ ln ( 1 ) + 2 ( ln ( 5 4 ) ) + 2 ( ln ( 3 2 ) ) + 2 ( ln ( 7 4 ) ) + ln ( 2 ) ] = 1 8 [ 0 + ( 2 ln ( 5 ) − 2 ln ( 4 ) ) + ( 2 ln ( 3 ) − 2 ln ( 2 ) ) + ( 2 ln ( 7 ) − 2 ln ( 4 ) ) + ln ( 2 ) ] = 1 8 [ 0 + 0.446287 + 0.810930 + 1.119232 + 0.693147 ] Simplify further, ∫ 1 2 ln x d x = 3

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

10th Edition

ISBN: 9781285464640

Author: Soo T. Tan

Publisher: Brooks Cole

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 7.3, Problem 13E

To determine

To approximate: The value of definite integral by using Trapezoidal Rule and Simpson’s Rule and compare the result with the exact value of the integral.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.3, Problem 12E

Chapter 7.3, Problem 14E

Students have asked these similar questions

3 points Save A Evaluate the definite integral/- -dx, where a=9, b31 and c=7. Write your b+cx2 ax answer up to two decimal places.

Explain each step carefully

Fundamental thereom of calc. Look at image:

Chapter 7 Solutions

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

Ch. 7.1 - Write the formula for integration by parts.Ch. 7.1 - Explain how you would choose u and dv when using...Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E

Ch. 7.1 - Prob. 9E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 26E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - In Exercises 29-34, evaluate each definite...Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Find the function f given that the slope of the...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Production of Steam Coal In keeping with the...Ch. 7.1 - Prob. 41E Ch. 7.1 - Concentration of a Drug in the Bloodstream The...Ch. 7.1 - Prob. 43E Ch. 7.1 - Average price of a Commodity The price of a...Ch. 7.1 - Distance Covered by a Car The velocity of the...Ch. 7.1 - Credit Card Losses in the United Kingdom The mail...Ch. 7.1 - U.S. Smartphone Users Smartphone users, as a...Ch. 7.1 - Prob. 49E Ch. 7.1 - Future Value of AN Investment Laura, the sole...Ch. 7.1 - Rate of Return on an Investment Suppose an...Ch. 7.1 - Present Value of A Franchise Tracy purchased a...Ch. 7.1 - Gini Index Refer to Section 6.7. The income...Ch. 7.1 - Prob. 56E Ch. 7.1 - A Mixture Problem Two tanks are connected in...Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - Prob. 62E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Producers' SURPLUS for WOMEN'S Boots Refer to...Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.3 - Explain why n can be odd or even in the...Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - In Exercises 23-28, find a bound on the error in...Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Condominium Resort Complex Cooper Realty is...Ch. 7.3 - AVERAGE Temperature The graph depicted ill the...Ch. 7.3 - Surface area of the Jacqueline Kennedy Onassis...Ch. 7.3 - Fuel Consumption of Domestic Cars Thanks to...Ch. 7.3 - Prob. 34E Ch. 7.3 - Medical Costs for Veterans According to a study by...Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Consumers Surplus Refer to Section 6.7. Before the...Ch. 7.3 - Prob. 39E Ch. 7.3 - Consumers Surplus for Sports Watches Refer to...Ch. 7.3 - PRODUCERS SURPLUS FOR CDs Refer to Section 6.7....Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Producers Surplus Refer to Section 6.7....Ch. 7.3 - Measuring Cardiac Output Eight milligrams of a dye...Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - In Exercises 50-53, determine whether the...Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.4 - a. Define 0f(x)dx, where f is continuous on [a, )...Ch. 7.4 - Prob. 2CQ Ch. 7.4 - In Exercises 1-4, find the area of the shaded...Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - In Exercises 5-14. find the area of the region...Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - THE AMOUNT OF an ENDOWMENT A university alumni...Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - PERPETUAL NET INCOME STREAMS The present value of...Ch. 7.4 - ESTABLISHING A TRUST FUND Becky Wilkinson wants to...Ch. 7.4 - PERPETUAL NET INCOME STREAM The perpetual stream...Ch. 7.4 - Prob. 53E Ch. 7.4 - Prob. 54E Ch. 7.4 - In Exercises 5356, determine whether the statement...Ch. 7.4 - Prob. 56E Ch. 7.4 - Prob. 57E Ch. 7.4 - Prob. 58E Ch. 7.4 - Prob. 59E Ch. 7.4 - Prob. 60E Ch. 7.5 - Prob. 1CQ Ch. 7.5 - Prob. 2CQ Ch. 7.5 - Prob. 1E Ch. 7.5 - Prob. 2E Ch. 7.5 - Prob. 3E Ch. 7.5 - Prob. 4E Ch. 7.5 - Prob. 5E Ch. 7.5 - Prob. 6E Ch. 7.5 - Prob. 7E Ch. 7.5 - Prob. 8E Ch. 7.5 - Prob. 9E Ch. 7.5 - Prob. 10E Ch. 7.5 - Prob. 11E Ch. 7.5 - Prob. 12E Ch. 7.5 - Prob. 13E Ch. 7.5 - Prob. 14E Ch. 7.5 - Prob. 15E Ch. 7.5 - Prob. 16E Ch. 7.5 - Prob. 17E Ch. 7.5 - Prob. 18E Ch. 7.5 - Prob. 19E Ch. 7.5 - Prob. 20E Ch. 7.5 - In Exercises 19-26, f is the probability density...Ch. 7.5 - Prob. 22E Ch. 7.5 - Prob. 23E Ch. 7.5 - In Exercises 19-26, f is the probability density...Ch. 7.5 - Prob. 25E Ch. 7.5 - Prob. 26E Ch. 7.5 - Prob. 27E Ch. 7.5 - Prob. 28E Ch. 7.5 - Prob. 29E Ch. 7.5 - Prob. 30E Ch. 7.5 - Prob. 31E Ch. 7.5 - Prob. 32E Ch. 7.5 - In Exercises 27-40, find the expected value of the...Ch. 7.5 - Prob. 34E Ch. 7.5 - Prob. 35E Ch. 7.5 - Prob. 36E Ch. 7.5 - Prob. 37E Ch. 7.5 - Prob. 38E Ch. 7.5 - Prob. 39E Ch. 7.5 - Prob. 40E Ch. 7.5 - WAITING Time AT A Health CLLNIC The average...Ch. 7.5 - Life Span of A Plant Species The life span of a...Ch. 7.5 - Product Reliability The tread life (in thousands...Ch. 7.5 - Prob. 44E Ch. 7.5 - Prob. 45E Ch. 7.5 - Prob. 46E Ch. 7.5 - Prob. 47E Ch. 7.5 - Prob. 48E Ch. 7.5 - Commuting Bill takes the commuter train to work...Ch. 7.5 - Musical Fountains Refer to Example 4. The...Ch. 7.5 - The Fountains OF Bellagio Refer to Example 4. The...Ch. 7.5 - Prob. 52E Ch. 7.5 - Reaction Time Of A Motorist The amount of time (in...Ch. 7.5 - Prob. 54E Ch. 7.5 - Prob. 55E Ch. 7.5 - Prob. 56E Ch. 7.5 - Prob. 57E Ch. 7.5 - Prob. 59E Ch. 7.5 - Prob. 60E Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Prob. 63E Ch. 7.5 - Prob. 64E Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 68E Ch. 7.5 - Prob. 69E Ch. 7.5 - Prob. 70E Ch. 7 - Fill in the blanks. 1. The integration by parts...Ch. 7 - Prob. 2CRQ Ch. 7 - Prob. 3CRQ Ch. 7 - Prob. 4CRQ Ch. 7 - Prob. 5CRQ Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Oil Spills Using aerial photographs, the Coast...Ch. 7 - Surface area OF a Lake a man-made lake located in...Ch. 7 - Prob. 40RE Ch. 7 - Prob. 1BM Ch. 7 - Prob. 2BM Ch. 7 - Prob. 3BM Ch. 7 - Prob. 4BM Ch. 7 - Prob. 5BM Ch. 7 - Prob. 6BM

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To approximate: The value of definite integral by using Trapezoidal Rule and Simpson’s Rule and compare the result with the exact value of the integral.

Solution Summary: The author compares the value of definite integral by using Trapezoidal Rule and Simpson’s Rule.

Concept explainers

Videos

To approximate: The value of definite integral by using Trapezoidal Rule and Simpson’s Rule and compare the result with the exact value of the integral.

Want to see the full answer?

Chapter 7 Solutions