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10th Edition

Ron Larson

Publisher: Cengage Learning

ISBN: 9781305860919

Chapter 6, Problem 1RE

Textbook Problem

**Integration by Parts** In Exercises 1–8, use integration by parts to find the indefinite integral.

Expert Solution

To determine

**To calculate:** The infinite integral of

**Solution:**

The infinite integral of

**Given Information:**

The provided integral is

**Formula used:**

The method of integration by parts:

If

Then,

Steps to solve the integral problems:

Step1: At first find the most complicated portion of the integrand and try to letter it as

Step2: First find the factor whose derivative is simple and consider it as

**Calculation:**

Recall the provided integral.

Observe from the above integrand that the simplest portion of the integrand is

Now consider

Therefore,

And,

Apply the integration by parts method.

Substitute

Hence, the infinite integral of

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Ch. 6.1 - Checkpoint 1 Find xe2xdx.Ch. 6.1 - Checkpoint 2 Find xlnxdx.Ch. 6.1 - Checkpoint 3 Find ln2xdx.Ch. 6.1 - Checkpoint 4 Find x3exdxCh. 6.1 - Checkpoint 5 Use the result of Example 4 to...Ch. 6.1 - Checkpoint 6 Use Example 6 to find the probability...Ch. 6.1 - Checkpoint 7 A company expects its income during...Ch. 6.1 - In Exercises 1-6, find f(x). f(x)=ln(x+1)Ch. 6.1 - In Exercises 1-6, find f(x). f(x)=ln(x2-1)Ch. 6.1 - In Exercises 1-6, find f(x). f(x)=ex2

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The...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Finding Present Value In Exercises 67-72, find the...Ch. 6.1 - Present Value You have just won $2,000,000 in a...Ch. 6.1 - Present Value You have just won $72,500,000 in a...Ch. 6.1 - Present Value A company expects its income c...Ch. 6.1 - Present Value A professional athlete signs a...Ch. 6.1 - Present Value A professional athlete signs a...Ch. 6.1 - HOW DO YOU SEE IT? 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(x13)2Ch. 6.2 - In Exercises 5 and 6, use integration by parts to...Ch. 6.2 - In Exercises 5 and 6, use integration by parts to...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 1-8, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 936, use the...Ch. 6.2 - Using Integration Tables In Exercises 9-36, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Finding Indefinite Integrals Using Two Methods In...Ch. 6.2 - Finding Indefinite Integrals Using Two Methods In...Ch. 6.2 - Finding Indefinite Integrals Using Two Methods In...Ch. 6.2 - Finding Indefinite Integrals Using Two Methods In...Ch. 6.2 - Probability The probability of recalling between a...Ch. 6.2 - Probability The probability of finding between a...Ch. 6.2 - Population Growth In Exercises 57 and 58, use a...Ch. 6.2 - Population Growth In Exercises 57 and 58, use a...Ch. 6.2 - Revenue The revenue (in dollars) for a new product...Ch. 6.2 - HOW DO YOU SEE IT? 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(Assume n is...Ch. 6.3 - In Exercises 9 and 10, solve for n. (Assume n is...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Surveying In Exercises 31 and 32, use the...Ch. 6.3 - Surveying In Exercises 31 and 32, use the...Ch. 6.3 - Error Analysis In Exercises 33-36, use the error...Ch. 6.3 - Error Analysis In Exercises 33-36, use the error...Ch. 6.3 - Error Analysis In Exercises 33-36, use the error...Ch. 6.3 - Error Analysis In Exercises 33-36, use the error...Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Median Age The table shows the median ages of the...Ch. 6.3 - Electricity The table shows the residential prices...Ch. 6.3 - Medicine A body assimilates a 12-hour cold tablet...Ch. 6.3 - HOW DO YOU SEE IT? The graph shows the weekly...Ch. 6.3 - Consumer Trends The rate of change in the number...Ch. 6.3 - Using Simpsons Rule Prove that Simpsons Rule is...Ch. 6.4 - Checkpoint 1 Determine the convergence or...Ch. 6.4 - Checkpoint 2 Evaluate the improper integral, if...Ch. 6.4 - Checkpoint 3 Evaluate the improper integral, if...Ch. 6.4 - Checkpoint 4 Use Example 4 to find the probability...Ch. 6.4 - Checkpoint 5 In Example 5, do you have enough...Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 1-6, find the limit (if it exists)....Ch. 6.4 - In Exercises 7-10, evaluate the expression (a)...Ch. 6.4 - In Exercises 7-10, evaluate the expression (a)...Ch. 6.4 - In Exercises 7-10, evaluate the expression (a)...Ch. 6.4 - In Exercises 7-10, evaluate the expression (a)...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Determining Whether an Integral Is Improper In...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 7-20,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 720,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 720,...Ch. 6.4 - Evaluating an Improper Integral In Exercises 720,...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Area of a Region In Exercises 21-26, find the area...Ch. 6.4 - Womens Height The mean height of American women...Ch. 6.4 - HOW DO YOU SEE IT? The graph shows the probability...Ch. 6.4 - Quality Control A company manufactures wooden...Ch. 6.4 - Quality Control A company manufactures compact...Ch. 6.4 - Endowment In Exercises 31-34, determine the amount...Ch. 6.4 - Endowment In Exercises 31-34, determine the amount...Ch. 6.4 - Endowment In Exercises 31-34, determine the amount...Ch. 6.4 - Endowment In Exercises 31-34, determine the amount...Ch. 6.4 - Scholarship Fund You want to start a scholarship...Ch. 6.4 - Charitable Foundation A charitable foundation...Ch. 6.4 - Present Value A business is expected to yield a...Ch. 6.4 - Present Value A farm is expected to yield a...Ch. 6.4 - Capitalized Cost In Exercises 3942, the...Ch. 6.4 - Capitalized Cost In Exercises 3942, the...Ch. 6.4 - Capitalized Cost In Exercises 39-42, the...Ch. 6.4 - Capitalized Cost In Exercises 39-42, the...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Integration by Parts In Exercises 18, use...Ch. 6 - Evaluating a Definite Integral In Exercises 912,...Ch. 6 - Evaluating a Definite integral In Exercises 912,...Ch. 6 - Evaluating a Definite integral In Exercises 912,...Ch. 6 - Evaluating a Definite Integral In Exercises 9-12,...Ch. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Finding Present Value In Exercises 13-16, find the...Ch. 6 - Present Value A company expects its income c...Ch. 6 - Present Value A company expects its income c...Ch. 6 - Using Integration Tables In Exercises 1922, use...Ch. 6 - Using Integration Tables In Exercises 1922, use...Ch. 6 - Using Integration Tables In Exercises 1922, use...Ch. 6 - Using Integration Tables In Exercises 1922, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 23-30, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 2330, use...Ch. 6 - Using Integration Tables In Exercises 31 and 32,...Ch. 6 - Using Integration Tables In Exercises 31 and 32,...Ch. 6 - Probability The probability of recalling between a...Ch. 6 - Probability The probability of locating between a...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6 - Error Analysis In Exercises 47 and 48, use the...Ch. 6 - Error Analysis In Exercises 47 and 48, use the...Ch. 6 - Error Analysis In Exercises 49 and 50, use the...Ch. 6 - Error Analysis In Exercises 49 and 50, use the...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Evaluating an Improper Integral In Exercises 5156,...Ch. 6 - Area of a Region In Exercises 5760, find the area...Ch. 6 - Area of a Region In Exercises 5760, find the area...Ch. 6 - Area of a Region In Exercises 5760, find the area...Ch. 6 - Area of a Region In Exercises 5760, find the area...Ch. 6 - Endowment In Exercises 61 and 62, determine the...Ch. 6 - Endowment In Exercises 61 and 62, determine the...Ch. 6 - Scholarship Fund You want to start a scholarship...Ch. 6 - Present Value You are considering buying a...Ch. 6 - In Exercises 13, use integration by parts to find...Ch. 6 - In Exercises 13, use integration by parts to find...Ch. 6 - In Exercises 13, use integration by parts to find...Ch. 6 - The sales S (in billions of dollars) for Dollar...Ch. 6 - In Exercises 57, use the integration table in...Ch. 6 - In Exercises 57, use the integration table in...Ch. 6 - In Exercises 57, use the integration table in...Ch. 6 - In Exercises 810, use integration by parts or the...Ch. 6 - In Exercises 810, use integration by parts or the...Ch. 6 - In Exercises 810, use integration by parts or the...Ch. 6 - Use Simpsons Rule with n=4 to approximate...Ch. 6 - Use Simpsons Rule with n=4 to approximate...Ch. 6 - Use the error formulas to find n such that the...Ch. 6 - In Exercises 1417, determine whether the improper...Ch. 6 - In Exercises 1417, determine whether the improper...Ch. 6 - In Exercises 1417, determine whether the improper...Ch. 6 - In Exercises 1417, determine whether the improper...Ch. 6 - A business is expected to yield a continuous flow...

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Reconsider the CI (7.10) for p, and focus on a confidence level of 95%. Show that the confidence limits agree q...

Probability and Statistics for Engineering and the Sciences

In the theory of relativity, the mass of a particle with velocity v is m0=m01v2/c2 where mo is the mass of the ...

Single Variable Calculus: Early Transcendentals

In Exercises 114, decide whether each of the given sets is a group with respect to the indicated operation. If ...

Elements Of Modern Algebra

In Exercises 21 to 32, solve each equation. 2x+3=17

Elementary Geometry For College Students, 7e

In addition, the numbers being added are known as ____________; the answer is known as the _______________. (1-...

Contemporary Mathematics for Business & Consumers

Perform the indicated operation and write each result in scientific notation: (9.51010)(4.61013)

Elementary Technical Mathematics

Sketch the graphs of each of the following between x=4 and x=4 by extending the graphs you made in Problems 13 ...

Trigonometry (MindTap Course List)

Finding an Indefinite Integral In Exercises 45-54, find the indefinite integral. csch(1/x)coth(1/x)x2dx

Calculus of a Single Variable

Comparing Integration Problems In Exercises 47-50, find the indefinite integrals, if possible, using the formul...

Calculus: Early Transcendental Functions (MindTap Course List)

Use a graphical utility to solve the system of equations using the rref or equivalent operation. 1.2x12.3x2+4.2...

Finite Mathematics for the Managerial, Life, and Social Sciences

In Exercises 33 to 36, we expand the list of trigonometric identities. As you may recall, an identity is a stat...

Elementary Geometry for College Students

Evaluating a Surface Integral In Exercises 9 and 10. evaluate sxydS. S:z=14x4,0x1,0yx2.

Calculus (MindTap Course List)

True or False:
If f(x) = f (−x) for all x then .

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

Finding the Arc Length of a Curve in Space In Exercises 59-62, sketch the space curve and find its length over ...

Multivariable Calculus

The direction cosines for the angles α, β, and γ in the figure are:
, ,
, ,
, ,
, ,

Study Guide for Stewart's Multivariable Calculus, 8th

Vacation occupancy rates were expected to be up during March 2008 in Myrtle Beach, South Carolina (The Sun News...

Statistics for Business & Economics, Revised (MindTap Course List)

In some studies, an investigator has n (x, y) pairs sampled from one population and m (x, y) pairs from a secon...

Introduction To Statistics And Data Analysis

Find each value of x. log7x=0

College Algebra (MindTap Course List)

Young children in the United States are exposed to an average of 4 hours of background television per day (CNN ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Describe the general characteristics of the case study design, identity the different situations for which this...

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the sine, cosine, or tangent functions of the following angels. Round the answers to 5 decimal places...

Mathematics For Machine Technology

Define and compute the three measures of central tendency.

Research Methods for the Behavioral Sciences (MindTap Course List)

4. In an experiment designed to test the output levels of three different treatments, the following results wer...

Essentials Of Statistics For Business & Economics

33. Consider the following two sets of rankings for six items.
Note that in the first case the rankings are id...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Answer Problems 110 without referring back to the text. Fill in the blank or answer true or false. 3. A constan...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

For each of the algorithm segments in 6—19, assume that n is a positive integer. (a) Compute the actual number ...

Discrete Mathematics With Applications

In Exercises 1-6, convert the information into a linear inequality. Give the meaning of each variable used. A b...

Mathematics: A Practical Odyssey

Reminder Round all answer to two decimal places unless otherwise indicated. Radioactive Decay For a certain rad...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

In the following exercises, compute the average value using the left Riemann sums LN for N = 1, 10, 100. How do...

Calculus Volume 2