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
![### Problem Statement
Given that
\[
\int_{4}^{6} f(x) \, dx = \frac{17}{7}
\]
find
\[
\int_{6}^{4} f(z) \, dz = \, \text{(Enter your answer here)}
\]
**Note:** No decimal entries allowed.
### Explanation
This problem requires you to evaluate the definite integral of a function in reverse order. You can use the property of definite integrals which states:
\[
\int_{a}^{b} f(x) \, dx = -\int_{b}^{a} f(x) \, dx
\]
Based on this property,
\[
\int_{6}^{4} f(z) \, dz = -\int_{4}^{6} f(x) \, dx
\]
Substituting the given value,
\[
\int_{6}^{4} f(z) \, dz = -\frac{17}{7}
\]
This results in the final answer:
\[
\int_{6}^{4} f(z) \, dz = -\frac{17}{7}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec70a3af-7012-41b5-84d0-077491201fef%2F6c53cfe0-0a51-4a33-873c-1f8ac93a2c2c%2F9agui6j_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
Given that
\[
\int_{4}^{6} f(x) \, dx = \frac{17}{7}
\]
find
\[
\int_{6}^{4} f(z) \, dz = \, \text{(Enter your answer here)}
\]
**Note:** No decimal entries allowed.
### Explanation
This problem requires you to evaluate the definite integral of a function in reverse order. You can use the property of definite integrals which states:
\[
\int_{a}^{b} f(x) \, dx = -\int_{b}^{a} f(x) \, dx
\]
Based on this property,
\[
\int_{6}^{4} f(z) \, dz = -\int_{4}^{6} f(x) \, dx
\]
Substituting the given value,
\[
\int_{6}^{4} f(z) \, dz = -\frac{17}{7}
\]
This results in the final answer:
\[
\int_{6}^{4} f(z) \, dz = -\frac{17}{7}
\]
Expert Solution
Step 1
We have to find
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning