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...
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![### Problem Statement:
**Find the integral**
\[ \int y \sqrt[5]{y} + 8 \, dy = \]
In this problem, you are required to calculate the indefinite integral of the function \( y \sqrt[5]{y} + 8 \) with respect to \( y \).
### Explanation:
- The integral symbol \(\int\) indicates that you need to integrate the given function.
- \( y \sqrt[5]{y} \) is a term where \( y \) is multiplied by the fifth root of \( y \).
- \( 8 \) is a constant term.
This integral combines polynomial terms and involves applying the power rule for integration. Write your answer by integrating each term separately and then combining the results.
### Steps to Solve:
1. Express \( y \sqrt[5]{y} \) as \( y^{1 + \frac{1}{5}} = y^{\frac{6}{5}} \).
2. Integrate \( y^{\frac{6}{5}} \) using the power rule.
3. Integrate the constant \( 8 \).
After integrating, combine the results to get the final solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e1b2c76-1760-4a7c-8b6e-bd7f0d0fa97d%2F2bb58700-14ad-4988-8121-64be30985b42%2Fcb49i9g_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement:
**Find the integral**
\[ \int y \sqrt[5]{y} + 8 \, dy = \]
In this problem, you are required to calculate the indefinite integral of the function \( y \sqrt[5]{y} + 8 \) with respect to \( y \).
### Explanation:
- The integral symbol \(\int\) indicates that you need to integrate the given function.
- \( y \sqrt[5]{y} \) is a term where \( y \) is multiplied by the fifth root of \( y \).
- \( 8 \) is a constant term.
This integral combines polynomial terms and involves applying the power rule for integration. Write your answer by integrating each term separately and then combining the results.
### Steps to Solve:
1. Express \( y \sqrt[5]{y} \) as \( y^{1 + \frac{1}{5}} = y^{\frac{6}{5}} \).
2. Integrate \( y^{\frac{6}{5}} \) using the power rule.
3. Integrate the constant \( 8 \).
After integrating, combine the results to get the final solution.
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