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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516
Chapter 8.8, Problem 87E
Textbook Problem
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Comparing Integrals

(a) Show that sin x d x diverges.

(b) Show that lim a a a sin x d x = 0 .

(c) What do parts (a) and (b) show about the definition ofimproper integrals?

(a)

To determine

To prove: The integral sinxdx diverges.

Explanation of Solution

Given: sinxdx

Formula used:

sinxdx=cosx+c

The limit formula for continuous function:

limxcf(x)=f(c)

Proof:

The given integral can be solved as:

sinxdx=0sinxdx+0sinxdx=limaa0sinxdx+limb

(b)

To determine

To prove: The limit limaaasinxdx=0.

(c)

To determine
The information given by part (a) and (b) about improper integrals.

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Chapter 8 Solutions

Calculus: Early Transcendental Functions
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Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In ExercisesIS-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercise 15-46,...Ch. 8.1 - Choosing a Formula In Exercises 5-14, select the...Ch. 8.1 - Finding an Indefinite Integral In Exercise 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercise15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Finding an Indefinite Integral In Exercises 15-46,...Ch. 8.1 - Slope Field In Exercises 47 and 48, a differential...Ch. 8.1 - Slope Field In Exercises 47 and 48, a differential...Ch. 8.1 - Slope -Field In-Exercises -49 -and-50, use a...Ch. 8.1 - Slope-Field In Exercises-49 and-50, use a computer...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Differential Equation In Exercises 51-56, find the...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Evaluating a Definite Integral In Exercises57-72,...Ch. 8.1 - Aiea In Exercise* 73-76, find the area of the...Ch. 8.1 - Area In Exercises 73-76, find the area or the...Ch. 8.1 - Area In Exercises 73-76, find the area of the...Ch. 8.1 - Area In Exercises 73-76, find the area the of the...Ch. 8.1 - Finding an Integral Using Technology In Exercises...Ch. 8.1 - Finding an Integra Using Technology In Exercises...Ch. 8.1 - Finding an Integral Using Technology In Exercises...Ch. 8.1 - Finding an Integral Using Technology In Exercises...Ch. 8.1 - Think About It When evaluating 11x2dx is it...Ch. 8.1 - Deriving a Rule Show that secx=sinxcosx+cosx1+sinx...Ch. 8.1 - Finding Constants Determine the constants a and b...Ch. 8.1 - Area The graphs of f(x)=x and g(x)=ex2 intersect...Ch. 8.1 - Comparing Antiderivatives (a) Explain why the...Ch. 8.1 - HOW DO YOU SEE IT? 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Use the graph of f shown in the...Ch. 8.3 - Area In Exercises 71 and 72, find the area of the...Ch. 8.3 - Area In Exercises 71 and 72, find the area of the...Ch. 8.3 - Area In Exercises 73 and 74, find the area of the...Ch. 8.3 - Area In Exercises 73 and 74, find the area of the...Ch. 8.3 - Volume In Exercises 75 and 76, find the volume of...Ch. 8.3 - Volume In Exercises 75 and 76, find the volume of...Ch. 8.3 - Volume and Centroid In Exercises 77 and 78, for...Ch. 8.3 - Volume and Centroid In Exercises 77 and 78, for...Ch. 8.3 - Verifying a Reduction Formula In Exercises 79-82,...Ch. 8.3 - Verifying a Reduction Formula In Exercises 79-82,...Ch. 8.3 - Verifying a Reduction Formula In Exercises 79-82,...Ch. 8.3 - Verifying a Reduction Formula In Exercises 79-82,...Ch. 8.3 - Using Formulas In Exercises 83-86, Find the...Ch. 8.3 - Using Formulas In Exercises 85-86, find the...Ch. 8.3 - Using Formulas In Exercises 83-86, find the...Ch. 8.3 - Using Formulas In Exercises 83-86, find the...Ch. 8.3 - Walliss Formulas Use the result of Exercise 80 to...Ch. 8.3 - Orthogonal Functions The inner product of two...Ch. 8.3 - Fourier Series The following sum is a finite...Ch. 8.4 - CONCEPT CHECK Trigonometric Substitution State the...Ch. 8.4 - Trigonometric Substitution:| Why -is Completing...Ch. 8.4 - Using trigonometric Substitution In Exercises 3-6,...Ch. 8.4 - Using trigonometric Substitution In Exercises 3-6,...Ch. 8.4 - Using trigonometric Substitution In Exercises 3-6,...Ch. 8.4 - Using trigonometric Substitution In Exercises 3-6,...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Using Trigonometric Substitution In Exercises...Ch. 8.4 - Special Integration Formulas In Exercises 15-18,...Ch. 8.4 - Special Integration Formulas In Exercises 15-18,...Ch. 8.4 - Special Integration Formulas In Exercises 15-18,...Ch. 8.4 - Special Integration Formulas In Exercises 15-18,...Ch. 8.4 - Finding an Indefinite Integral In Exercises 19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises 19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises 19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises 19-32,...Ch. 8.4 - Finding an Indefinite Integral In Exercises 19-32,...Ch. 8.4 - Completing the Square In Exercises 33-36, find the...Ch. 8.4 - Completing the Square In Exercises 33-36, complete...Ch. 8.4 - Completing the Square In Exercises 33-36, find the...Ch. 8.4 - Completing the Square In Exercises 33-36, find the...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - Converting the Limits of Integration In Exercises...Ch. 8.4 - EXPLORING CONCEPTS xx2+1dxCh. 8.4 - EXPLORING CONCEPTS x2x21dxCh. 8.4 - Comparing Methods (a) Find the integral x1x2dx dx...Ch. 8.4 - How do you see it? Use the graph of f1 shown in...Ch. 8.4 - True or False? In Exercises 47-50, determine...Ch. 8.4 - True or False? In Exercises 47-50, determine...Ch. 8.4 - True or False? In Exercise 47-50 Determine whether...Ch. 8.4 - True or False? In Exercise 47-50 Determine whether...Ch. 8.4 - Area Find the Area enclosed by the ellipse...Ch. 8.4 - Area Find the area of the shaded region of the...Ch. 8.4 - Arc Length In Exercises 53 and 54, find the arc...Ch. 8.4 - Arc Length In Exercises 53 and 54, find the arc...Ch. 8.4 - Volume of a Torus In Exercises 55 and 56, find the...Ch. 8.4 - Volume of a Torus In Exercises 55 and 56, find the...Ch. 8.4 - Centroid In Exercises 57 and 58, find the centroid...Ch. 8.4 - Centroid In Exercise 57 and 58, Find the Centroid...Ch. 8.4 - Volume The axis of a storage tank in the form of a...Ch. 8.4 - Field Strength The field strength H of a magnet of...Ch. 8.4 - Tractrix A person moves from the origin along the...Ch. 8.4 - Conjecture (a) Find formulas for the distances...Ch. 8.4 - Fluid Force Find the fluid force on a circular...Ch. 8.4 - Fluid Force Evaluate the following two integrals,...Ch. 8.4 - Verifying Formulas Use trigonometric substitution...Ch. 8.4 - Arc length show that the arc length of the graph...Ch. 8.4 - Area of a Lune The crescent shaped region bounded...Ch. 8.4 - Area: Two circles of radius 3, with centres at...Ch. 8.4 - Evaluate 01ln(x+1)x2+1dxCh. 8.5 - CONCEPT CHECK Partial Fraction Decomposition:...Ch. 8.5 - Guidelines for Solving the Basic Equation In your...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using Partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using partial Fractions In Exercises 3-20, use...Ch. 8.5 - Using partial Fractions In Exercises 3-20, use...Ch. 8.5 - Evaluating a Definite Integral In Exercises 2124,...Ch. 8.5 - Evaluating a Definite Integral In Exercises 21-24,...Ch. 8.5 - Evaluating a Definite Integral In Exercises 21-24,...Ch. 8.5 - Evaluating a Definite Integral In exercises 21-24,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Finding an Indefinite Integral In Exercises 25-32,...Ch. 8.5 - Verifying a Formula In Exercises 33-36, use the...Ch. 8.5 - Verifying a Formula In Exercises 33-36, use the...Ch. 8.5 - Verifying a Formula In Exercises 33-36, use the...Ch. 8.5 - Verifying a Formula In Exercises 33-36, use the...Ch. 8.5 - EXPLORING CONCEPTS Choosing a method In Exercises...Ch. 8.5 - EXPLORING CONCEPTS Choosing a method In Exercises...Ch. 8.5 - EXPLORING CONCEPTS Choosing a method In Exercises...Ch. 8.5 - HOW DO YOU SEE IT? Use the graph of f1 shown in...Ch. 8.5 - Area In Exercises 41-44, use partial fractions to...Ch. 8.5 - Area In Exercises 41-44, use partial Tractions to...Ch. 8.5 - Area In Exercises 41-44, use partial Tractions to...Ch. 8.5 - Area In Exercises 41-44, use partial Tractions to...Ch. 8.5 - Modeling Data The predicted cost C (in hundreds of...Ch. 8.5 - Average Value of a Function Find the average value...Ch. 8.5 - Volume and Centroid Consider the region bounded by...Ch. 8.5 - Volume Consider the region bounded by the graph of...Ch. 8.5 - Epidemic Model A single infected individual enters...Ch. 8.5 - Chemical Reaction In a chemical reaction, one unit...Ch. 8.5 - Using Two Methods Evaluce 01x1+x4dx in two...Ch. 8.5 - Prove 227=01x4(1x)41+x2dxCh. 8.5 - Let p(x) be a nonzero polynomial of degree less...Ch. 8.6 - CONCEPT CHECK Finding an Interval Would you use...Ch. 8.6 - CONCEPT CHECK Errors in the Trapezoidal Rule and...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpson's Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 8.6 - Estimating Errors In Exercises 25-28, use the...Ch. 8.6 - Estimating Errors In Exercises 25-28, use the...Ch. 8.6 - Estimating Errors In Exercises 25-28, use the...Ch. 8.6 - Estimating Errors In Exercises 25-28, use the...Ch. 8.6 - Estimating Errors In Exercises 29-32, use the...Ch. 8.6 - Estimating Errors In Exercises 29-32, use the...Ch. 8.6 - Estimating Errors In Exercises 29-32, use the...Ch. 8.6 - Estimating Errors In Exercises 29-32, use the...Ch. 8.6 - Estimating Errors Using Technology In Exercises 33...Ch. 8.6 - Estimating Errors Using Technology In Exercises 33...Ch. 8.6 - Finding the Area of a Region Approximate the area...Ch. 8.6 - Finding the Area of a Region Approximate the area...Ch. 8.6 - Area Use Simpsons Rule with n=14 to approximate...Ch. 8.6 - HOW DO YOU SEE IT? The function f is concave...Ch. 8.6 - EXPLORING CONCEPTS Think About It Explain how the...Ch. 8.6 - EXPLORING CONCEPTS Describing an Error Describe...Ch. 8.6 - Surveying Use the Trapezoidal Rule to estimate the...Ch. 8.6 - Circumference The elliptic integral 830/2112sin2dCh. 8.6 - Work To determine the size of the motor required...Ch. 8.6 - Approximating a Function The table lists...Ch. 8.6 - Proof Prove that Simpsons Rule is exact...Ch. 8.6 - Proof Prove that you can find a polynomial...Ch. 8.7 - CONCEPT CHECK Integration by Tables Which formula...Ch. 8.7 - CONCEPT CHECK Reduction Formula Describe what is...Ch. 8.7 - Integration by Tables In Exercises 3 and 4, use a...Ch. 8.7 - Integration by Tables In Exercises 3 and 4, use a...Ch. 8.7 - Integration by Tables In Exercises 5 and 6, use a...Ch. 8.7 - Integration by Tables In Exercises 5 and 6, use a...Ch. 8.7 - Integration by Tables In Exercises 7-10, use a...Ch. 8.7 - Integration by Tables In Exercises 7-10, use a...Ch. 8.7 - Integration by Tables In Exercises 7-10, use a...Ch. 8.7 - Integration by Tables In Exercises 7-10, use a...Ch. 8.7 - Integration by Tables In Exercises 11 and 12, use...Ch. 8.7 - Integration by Tables In Exercises 11 and 12, use...Ch. 8.7 - Integration by Tables In Exercises 13 and 14, use...Ch. 8.7 - Integration by Tables In Exercises 13 and 14, use...Ch. 8.7 - Using Two Methods In Exercises 15-18, find the...Ch. 8.7 - Using Two Methods In Exercises 15-18, find the...Ch. 8.7 - Using Two Methods In Exercises 15-18, find the...Ch. 8.7 - Using Two Methods In Exercises 15-18, find the...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Finding an Indefinite Integral In Exercises 19-40,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Evaluating a Definite Integral In Exercises41-48,...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Verifying a Formula In Exercises 49-54, verify...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Finding or Evaluating an Integral In Exercises...Ch. 8.7 - Area In Exercises 63 and 64, find the area of the...Ch. 8.7 - Area In Exercises 63 and 64, find the area of the...Ch. 8.7 - EXPLORING CONCEPTS Finding a Pattern (a) Find...Ch. 8.7 - EXPLORING CONCEPTS Choosing a Method State the...Ch. 8.7 - Work A hydraulic cylinder on an industrial machine...Ch. 8.7 - Work Repeat Exercise 67, using F(x)=500x26x2...Ch. 8.7 - Population A population is growing according to...Ch. 8.7 - HOW DO YOU SEE IT? Use the graph of f shown in the...Ch. 8.7 - Volume Consider the region bounded by the graphs...Ch. 8.7 - Building Design The cross section of a precast...Ch. 8.7 - PUTNAM EXAM CHALLENGE Evaluate 0/2dx1+(tanx)2....Ch. 8.8 - CONCEPT CHECK Improper Integrals Describe two ways...Ch. 8.8 - CONCEPT CHECK Improper Integrals What does it mean...Ch. 8.8 - CONCEPT CHECK Indefinite Integration Limits...Ch. 8.8 - CONCEPT CHECK Finding Values For what values of a...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Determining Whether an Integral Is Improper In...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Evaluating an Improper Integral In Exercises...Ch. 8.8 - Finding Values In Exercises 49 and 50, determine...Ch. 8.8 - Finding Values In Exercises 49 and 50, determine...Ch. 8.8 - Mathematical Induction Use mathematical...Ch. 8.8 - Comparison Test for Improper Integrals In...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - Convergence or Divergence In Exercises 53-60, use...Ch. 8.8 - EXPLORING CONCEPTS Improper IntegralExplain why...Ch. 8.8 - EXPLORING CONCEPTS Improper Integral Consider the...Ch. 8.8 - Area In Exercises 63-66, find the area of...Ch. 8.8 - Area In Exercises 63-66, find the area of...Ch. 8.8 - Area In Exercises 63-66, find the area of...Ch. 8.8 - Area In Exercises 63-66, find the area of...Ch. 8.8 - Area and Volume In Exercises 67 and 68, consider...Ch. 8.8 - Area and Volume In Exercises 67 and 68, consider...Ch. 8.8 - Arc Length Find the arc length of the graph of...Ch. 8.8 - Surface Area Find the area of the surface formed...Ch. 8.8 - Propulsion In Exercises 71 and 72, use the weight...Ch. 8.8 - Propulsion In Exercises 71 and 72, use the weight...Ch. 8.8 - In Exercises 73 and 74, (a) show that the...Ch. 8.8 - In Exercises 73 and 74, (a) show that the...Ch. 8.8 - Normal Probability The mean height of American...Ch. 8.8 - HOW DO YOU SEE IT? The graph shows the probability...Ch. 8.8 - Capitalized Cost In Exercises 77 and 78, find the...Ch. 8.8 - Capitalized Cost In Exercises 77 and 78, find the...Ch. 8.8 - Electromagnetic Theory The magnetic potential P at...Ch. 8.8 - Gravitational Force A semi-infinite uniform...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - True or False? In Exercises 81-86, determine...Ch. 8.8 - Comparing Integrals (a) Show that sinxdx diverges....Ch. 8.8 - Exploration Consider the integral 0/241+(tanx)ndx...Ch. 8.8 - Comparing Integrals Let f be continuous on the...Ch. 8.8 - Writing (a) The improper integrals 11xdxand11x2dx...Ch. 8.8 - when the improper integral exists. Laplace...Ch. 8.8 - when the improper integral exists. 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Laplace...Ch. 8.8 - The Gamma Function The Gamma Function (n)...Ch. 8.8 - Proof Prove that In=(n1n+2)In1, where...Ch. 8.8 - Finding a Value For what value of e does the...Ch. 8.8 - Finding a Value For what value of c does the...Ch. 8.8 - Volume Find the volume of the solid generated by...Ch. 8.8 - Volume Find the volume of the solid generated...Ch. 8.8 - u-Substitution In Exercises 105 and 106, rewrite...Ch. 8.8 - u-Substitution In Exercises 105 and 106, rewrite...Ch. 8.8 - Rewriting an Integral Let f(x)dx be convergent and...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - Using Basic Integration Rules In Exercises 1-8,...Ch. 8 - 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Area In Exercises 27 and 28, find the area of the...Ch. 8 - Area In Exercises 27 and 28, find the area of the...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Trigonometric Substitution In Exercises...Ch. 8 - Using Different Methods In Exercises 35 and 36,...Ch. 8 - Using Different Methods In Exercises 35 and 36,...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - Using Partial Fractions In Exercises 37-44, use...Ch. 8 - 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Finding an Indefinite Integral In Exercises 57-64,...Ch. 8 - Finding an Indefinite Integral In Exercises 57-64,...Ch. 8 - Differential Equation In Exercises 65-68, find the...Ch. 8 - Differential Equation In Exercises 65-68, find the...Ch. 8 - Differential Equation In Exercises 65-68, find the...Ch. 8 - Differential Equation In Exercises 65-68, find the...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Evaluating a Definite Integral In Exercises 69-74,...Ch. 8 - Area In Exercises 75 and 76, find the area of the...Ch. 8 - Area In Exercises 75 and 76, find the area of the...Ch. 8 - Centroid In Exercises 77 and 78, find the centroid...Ch. 8 - Centroid In Exercises 77 and 78, find the centroid...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Evaluating an Improper Integral In Exercises...Ch. 8 - Present Value The board of directors of a...Ch. 8 - Volume Find the volume of the solid generated by...Ch. 8 - Probability The average lengths (from beak to...Ch. 8 - Walliss Formulas (a) Evaluate the integrals...Ch. 8 - Proof (a) Evaluate the integrals...Ch. 8 - Comparing Methods Let I=04f(x)dx, where f is shown...Ch. 8 - Area Consider the problem of finding the area of...Ch. 8 - Area Use the substitution u=tanx2 to find the area...Ch. 8 - Arc Length Find the arc length of the graph of the...Ch. 8 - Centroid Find the centroid of the region bounded...Ch. 8 - Proof Prove the following generalization of the...Ch. 8 - Inverse Function and Area (a) Let y=f1(x) be the...Ch. 8 - Area Factor the polynomial p(x)=x4+1 and then find...Ch. 8 - Partial Fraction Decomposition Suppose the...Ch. 8 - Partial Fraction Decomposition Use the result of...Ch. 8 - Evaluating an Integral (a) Use the substitution...Ch. 8 - Elementary Functions Some elementary functions,...Ch. 8 - Rocket The velocity v (in feet per second) of a...Ch. 8 - Proof Suppose that f(a)=f(b)=g(a)=g(b)=0 and the...Ch. 8 - Proof Suppose that f(a)=f(b)=0 and the second...Ch. 8 - Approximating an Integral Using the inequality...Ch. 8 - Volume Consider die shaded region between die...

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