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
![### Integral Transformation Example
Consider the following integral:
\[ \int \frac{-\sin(y)}{\cos(y) + 7} \, dy \]
This can be transformed into a basic integral by letting:
\[ u = \cos(y) + 7 \]
\[ du = -\sin(y) \, dy \]
After performing the substitution, you obtain the integral:
\[ \int \frac{du}{u} \]
However, there is an error message that says:
```
syntax error. Check your variables - you might be using a
```
For assistance, you can either message the instructor or submit your question for further help.
**Action Buttons:**
- **Message instructor**: Send a question to your instructor for personalized help.
- **Add Work**: An option to add your additional workings or notes.
- **Submit Question**: Submit the question for review or assistance.
**Additional Features:**
- The "Next question" button allows you to move to another problem.
- The "Get a similar question" button helps in practicing more problems of the same type.
- Below the instructions, there is a placeholder where you can type here to search for more information or resources online.
### Explanation:
To solve the given integral \( \int \frac{-\sin(y)}{\cos(y) + 7} \, dy \), follow these steps:
1. **Identify the substitution** to simplify the integral. In this case, let \( u = \cos(y) + 7 \).
2. **Calculate \( du \)** by differentiating \( u \) with respect to \( y \):
\[ du = -\sin(y) \, dy \]
3. Substitute \( u \) and \( du \) into the integral:
\[ \int \frac{du}{u} \]
4. Resolve any syntax errors by checking the variable definitions and ensuring they are correctly applied in the integral transformation.
By transforming the integral into a simpler form, it becomes easier to solve using standard integral techniques.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4a5f554e-4271-4f0d-9ea6-a64eb74e1bc6%2Fb4dfdc6c-c45f-4ab3-9908-df8081370658%2Fm3wmy1k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Integral Transformation Example
Consider the following integral:
\[ \int \frac{-\sin(y)}{\cos(y) + 7} \, dy \]
This can be transformed into a basic integral by letting:
\[ u = \cos(y) + 7 \]
\[ du = -\sin(y) \, dy \]
After performing the substitution, you obtain the integral:
\[ \int \frac{du}{u} \]
However, there is an error message that says:
```
syntax error. Check your variables - you might be using a
```
For assistance, you can either message the instructor or submit your question for further help.
**Action Buttons:**
- **Message instructor**: Send a question to your instructor for personalized help.
- **Add Work**: An option to add your additional workings or notes.
- **Submit Question**: Submit the question for review or assistance.
**Additional Features:**
- The "Next question" button allows you to move to another problem.
- The "Get a similar question" button helps in practicing more problems of the same type.
- Below the instructions, there is a placeholder where you can type here to search for more information or resources online.
### Explanation:
To solve the given integral \( \int \frac{-\sin(y)}{\cos(y) + 7} \, dy \), follow these steps:
1. **Identify the substitution** to simplify the integral. In this case, let \( u = \cos(y) + 7 \).
2. **Calculate \( du \)** by differentiating \( u \) with respect to \( y \):
\[ du = -\sin(y) \, dy \]
3. Substitute \( u \) and \( du \) into the integral:
\[ \int \frac{du}{u} \]
4. Resolve any syntax errors by checking the variable definitions and ensuring they are correctly applied in the integral transformation.
By transforming the integral into a simpler form, it becomes easier to solve using standard integral techniques.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.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