Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
Bartleby Related Questions Icon

Related questions

Q: Which of the following is the equation of a line perpendicular to x + 3y = -17 and passing through…
A:
Q: don't understand why the -x disappears for the left side of the product rule procedure for the…
A: f(x) = xlnx -x Here the product rule applied on the term (x lnx) only. f'(x) = d/dx (xlnx) + d/dx…
Q: Sorry, this
A:
Q: what if y(0) = 6 instead?
A:
Q: What is the slope-intercept form of the equation -4x + 2y = 8? OA.y = 4x 2 HE OB. y=-4x+8 Ocy 2x +4…
A: The given equation is. -4x+2y=8
Q: What is the are between the graph of y=4x³+2 and the x-axis from x=1 to x=2
A:
Q: Graph 4x - 5y = 20 and identify the x-intercept as an ordered pair. O x-int:
A:
Q: Negative 45 multiplied by an unknown number combined with 12 is less than 117.
A: Given,           Negative 45 multiplied by an unknown number combined with 12            is less…
Q: 6. Give the equation for the following (-2,0) y X
A:
Q: 3. y = x2 - 2 -3 -2 -10 3D 2 3 X
A:
Q: REMOVE THE PARENTHESIS FROM THE FOLLOWING EQUATION x-(-y-z+3)
A:
Q: i am having trouble with  finding the x-intercept of  y = x3 + 2 (-1.26, 0) is the closest i got
A: To determine the x-intercept, we set y equal to zero and solve for x.
Q: Not exactly sure if X=0 is the inflection point or if x=0 and x=4 are the inflection points. If x=0…
A: We have to find point of inflection
Q: (2n)! a"(n!)2 A) diverges if |a| 2² n-1 C) converges if |a| > 2ª
A: Here we have to find the converges or diverges of the given series.
Q: Calculate y" for y=12x3-5x2+3x
A:
Q: If i have the problem 4y - x = -4 , how do I write this in slope intercept form?
A: The given equation is
Q: Where the graph y = x^3 − 3x^2 + 2x − 10 is concave up and concave down?
A:
Question
How can I get rid of the highlighted x in this u-substitution problem?
## Integration by Substitution Example This example demonstrates how to use substitution for the integration of \( \int \sec^3{x} \tan{x} \, dx \). ### Step-by-Step Solution: 1. Begin with the integral: \[ \int \sec^3{x} \tan{x} \, dx \] 2. Introduce a substitution: Let \( u = \tan{x} \) which implies that \( du = \sec^2{x} \, dx \). Rearranging for \( dx \), we get: \[ dx = \frac{1}{\sec^2{x}} \, du \] 3. Substitute \( u \) and \( dx \) into the integral: Since \( \sec^3{x} = \sec{x} \cdot \sec^2{x} \), the integral becomes: \[ \int \frac{\sec^3{x} \cdot u}{\sec^2{x}} \, du \] 4. Simplify the expression: \[ \int \sec{x} \cdot u \, du \] At this point, there is a remaining \( \sec{x} \) term, despite substituting \( dx \). 5. Identifying the problem: There is a highlighted text in the image indicating: *How to get rid of this \( x \)?* To handle the extra \(\sec{x}\) term in \( \sec{x} \cdot u \, du \), note that \(\sec{x} = \sqrt{u^2 + 1}\) because \(\sec^2{x} = 1 + \tan^2{x}\). ### Summary To complete the integral, substitute \(\sec{x}\) using the relation to \( u \): \[ \sec{x} = \sqrt{1 + u^2} \] Transforming the integral fully in terms of \( u \): \[ \int \sqrt{1 + u^2} \, u \, du \] The final result requires further simplification or a different technique to integrate the expression completely.
expand button
Transcribed Image Text:## Integration by Substitution Example This example demonstrates how to use substitution for the integration of \( \int \sec^3{x} \tan{x} \, dx \). ### Step-by-Step Solution: 1. Begin with the integral: \[ \int \sec^3{x} \tan{x} \, dx \] 2. Introduce a substitution: Let \( u = \tan{x} \) which implies that \( du = \sec^2{x} \, dx \). Rearranging for \( dx \), we get: \[ dx = \frac{1}{\sec^2{x}} \, du \] 3. Substitute \( u \) and \( dx \) into the integral: Since \( \sec^3{x} = \sec{x} \cdot \sec^2{x} \), the integral becomes: \[ \int \frac{\sec^3{x} \cdot u}{\sec^2{x}} \, du \] 4. Simplify the expression: \[ \int \sec{x} \cdot u \, du \] At this point, there is a remaining \( \sec{x} \) term, despite substituting \( dx \). 5. Identifying the problem: There is a highlighted text in the image indicating: *How to get rid of this \( x \)?* To handle the extra \(\sec{x}\) term in \( \sec{x} \cdot u \, du \), note that \(\sec{x} = \sqrt{u^2 + 1}\) because \(\sec^2{x} = 1 + \tan^2{x}\). ### Summary To complete the integral, substitute \(\sec{x}\) using the relation to \( u \): \[ \sec{x} = \sqrt{1 + u^2} \] Transforming the integral fully in terms of \( u \): \[ \int \sqrt{1 + u^2} \, u \, du \] The final result requires further simplification or a different technique to integrate the expression completely.
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
See solutionCheck out a sample Q&A here
Step 1
VIEW
Step 2
VIEW
bartleby

Step by stepSolved in 2 steps with 2 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
SEE MORE TEXTBOOKS