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:
\[ \int (4x^7 + 6x^6) \, dx \]
**Solution:**
To solve this integral, use the power rule for integration, which states:
\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C
\]
Applying the rule to each term:
1. For \(4x^7\), integrate to get \(\frac{4x^8}{8} = \frac{x^8}{2}\).
2. For \(6x^6\), integrate to get \(\frac{6x^7}{7}\).
Thus, the integral becomes:
\[
\frac{x^8}{2} + \frac{6x^7}{7} + C
\]
where \(C\) is the constant of integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e006314-f9b9-42f4-83ad-7d314395efcf%2F8501a8f2-0df3-4b06-abcb-b10e3f7743d2%2Ffz9brd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find the integral:
\[ \int (4x^7 + 6x^6) \, dx \]
**Solution:**
To solve this integral, use the power rule for integration, which states:
\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C
\]
Applying the rule to each term:
1. For \(4x^7\), integrate to get \(\frac{4x^8}{8} = \frac{x^8}{2}\).
2. For \(6x^6\), integrate to get \(\frac{6x^7}{7}\).
Thus, the integral becomes:
\[
\frac{x^8}{2} + \frac{6x^7}{7} + C
\]
where \(C\) is the constant of integration.
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