4 dx using partial fractions. Factor the denominator of the integrand. 2-9 First evaluate 2 -9=0 Using the result of the previous step, rewrite the integrand using partial fraction decomposition. dx dx - 9 х-3 Solve for A and B. and B = (Type integers or simplified fractions.) Substitute the determined values for A and B into the integrand from a previous step and integrate. 4 dx x -9 4 dx Now evaluate using a trigonometric substitution. Because the integral contains the form x - a, use a secant substitution, where x= a sec 0. Determine the value of a. 2-9 x = a sec 0 Find dx. dx = Substitute the determined values for x and dx into the integrand and simplify completely. dx Integrate the result from the previous step. dx x -9 Rewrite the integral in terms of x and simplify the result. Use the reference triangle for the secant substitution shown here to determine the values. dx 4 x = a sec 0 Reconcile the results from the two evaluations of the integral. Choose the correct answer below. O A. The two results can be reconciled by using integration by parts. O B. The two results can be reconciled using the properties of logarithms. The two results can be reconciled because the secant substitution results in /tan e = - tan 0 in this case. O D. The two results can be reconciled by changing the constant of integration.
4 dx using partial fractions. Factor the denominator of the integrand. 2-9 First evaluate 2 -9=0 Using the result of the previous step, rewrite the integrand using partial fraction decomposition. dx dx - 9 х-3 Solve for A and B. and B = (Type integers or simplified fractions.) Substitute the determined values for A and B into the integrand from a previous step and integrate. 4 dx x -9 4 dx Now evaluate using a trigonometric substitution. Because the integral contains the form x - a, use a secant substitution, where x= a sec 0. Determine the value of a. 2-9 x = a sec 0 Find dx. dx = Substitute the determined values for x and dx into the integrand and simplify completely. dx Integrate the result from the previous step. dx x -9 Rewrite the integral in terms of x and simplify the result. Use the reference triangle for the secant substitution shown here to determine the values. dx 4 x = a sec 0 Reconcile the results from the two evaluations of the integral. Choose the correct answer below. O A. The two results can be reconciled by using integration by parts. O B. The two results can be reconciled using the properties of logarithms. The two results can be reconciled because the secant substitution results in /tan e = - tan 0 in this case. O D. The two results can be reconciled by changing the constant of integration.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![4 dx
using partial fractions. Factor the denominator of the integrand.
2-9
First evaluate
2 -9=0
Using the result of the previous step, rewrite the integrand using partial fraction decomposition.
dx
dx
- 9
х-3
Solve for A and B.
and B =
(Type integers or simplified fractions.)
Substitute the determined values for A and B into the integrand from a previous step and integrate.
4 dx
x -9
4 dx
Now evaluate
using a trigonometric substitution. Because the integral contains the form x - a, use a secant substitution, where x= a sec 0. Determine the value of a.
2-9
x = a sec 0
Find dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54144759-0e64-4a52-9eb8-f3918d0f39d7%2F1698d3d9-2c40-451d-a02d-a5dbee676c16%2Fz4ziqrf.jpeg&w=3840&q=75)
Transcribed Image Text:4 dx
using partial fractions. Factor the denominator of the integrand.
2-9
First evaluate
2 -9=0
Using the result of the previous step, rewrite the integrand using partial fraction decomposition.
dx
dx
- 9
х-3
Solve for A and B.
and B =
(Type integers or simplified fractions.)
Substitute the determined values for A and B into the integrand from a previous step and integrate.
4 dx
x -9
4 dx
Now evaluate
using a trigonometric substitution. Because the integral contains the form x - a, use a secant substitution, where x= a sec 0. Determine the value of a.
2-9
x = a sec 0
Find dx.
![dx =
Substitute the determined values for x and dx into the integrand and simplify completely.
dx
Integrate the result from the previous step.
dx
x -9
Rewrite the integral in terms of x and simplify the result. Use the reference triangle for the secant substitution shown here to determine the values.
dx
4
x = a sec 0
Reconcile the results from the two evaluations of the integral. Choose the correct answer below.
O A. The two results can be reconciled by using integration by parts.
O B. The two results can be reconciled using the properties of logarithms.
The two results can be reconciled because the secant substitution results in /tan e = - tan 0 in this case.
O D. The two results can be reconciled by changing the constant of integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54144759-0e64-4a52-9eb8-f3918d0f39d7%2F1698d3d9-2c40-451d-a02d-a5dbee676c16%2F2jjj4mh.jpeg&w=3840&q=75)
Transcribed Image Text:dx =
Substitute the determined values for x and dx into the integrand and simplify completely.
dx
Integrate the result from the previous step.
dx
x -9
Rewrite the integral in terms of x and simplify the result. Use the reference triangle for the secant substitution shown here to determine the values.
dx
4
x = a sec 0
Reconcile the results from the two evaluations of the integral. Choose the correct answer below.
O A. The two results can be reconciled by using integration by parts.
O B. The two results can be reconciled using the properties of logarithms.
The two results can be reconciled because the secant substitution results in /tan e = - tan 0 in this case.
O D. The two results can be reconciled by changing the constant of integration.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 8 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning