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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Question
![**Evaluate the following integral using integration by parts.**
\[
\int x \sin 6x \, dx
\]
**Options:**
- **A.** \(-\frac{1}{6} x \cos 6x + \int \left[ \frac{1}{6} \cos 6x \right] \, dx\)
- **B.** \(-\frac{1}{6} \cos 6x - \int \left(-\frac{1}{6} x \cos 6x \right) \, dx\)
- **C.** \(-\frac{1}{6} x \cos 6x - \int \left(-\frac{1}{6} \cos 6x \right) \, dx\)
- **D.** \(6x \cos \frac{1}{6} x + \int \left(6 \cos \frac{1}{6} x \right) \, dx\)
**Question:**
Evaluate the integral:
\[
\int x \sin 6x \, dx = \, \text{[Provide your answer here]}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F070e8b65-931e-44e7-bfb4-6d69e5ced655%2Fc0779c6f-db4e-4683-9ffb-e59cb5daba70%2Fyrjwmd8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the following integral using integration by parts.**
\[
\int x \sin 6x \, dx
\]
**Options:**
- **A.** \(-\frac{1}{6} x \cos 6x + \int \left[ \frac{1}{6} \cos 6x \right] \, dx\)
- **B.** \(-\frac{1}{6} \cos 6x - \int \left(-\frac{1}{6} x \cos 6x \right) \, dx\)
- **C.** \(-\frac{1}{6} x \cos 6x - \int \left(-\frac{1}{6} \cos 6x \right) \, dx\)
- **D.** \(6x \cos \frac{1}{6} x + \int \left(6 \cos \frac{1}{6} x \right) \, dx\)
**Question:**
Evaluate the integral:
\[
\int x \sin 6x \, dx = \, \text{[Provide your answer here]}
\]
![**Problem:**
Evaluate the following integral using integration by parts.
\[
\int x \sin 6x \, dx
\]
---
**Instructions:**
Use the integration by parts formula so that the new integral is simpler than the original one. Choose the correct answer below.
**Options:**
A. \(\frac{1}{6} x \cos 6x + \int \left(\frac{1}{6} \cos 6x \right) dx\)
B. \(-\frac{1}{6} \cos 6x - \int \left( -\frac{1}{6} x \cos 6x \right) dx\)
C. \(-\frac{1}{6} x \cos 6x - \int \left( -\frac{1}{6} \cos 6x \right) dx\)
D. \(6x \cos \frac{1}{6} x + \int \left(6 \cos \frac{1}{6} x \right) dx\)
**Task:**
Evaluate the integral.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F070e8b65-931e-44e7-bfb4-6d69e5ced655%2Fc0779c6f-db4e-4683-9ffb-e59cb5daba70%2Fdjp2ns_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Evaluate the following integral using integration by parts.
\[
\int x \sin 6x \, dx
\]
---
**Instructions:**
Use the integration by parts formula so that the new integral is simpler than the original one. Choose the correct answer below.
**Options:**
A. \(\frac{1}{6} x \cos 6x + \int \left(\frac{1}{6} \cos 6x \right) dx\)
B. \(-\frac{1}{6} \cos 6x - \int \left( -\frac{1}{6} x \cos 6x \right) dx\)
C. \(-\frac{1}{6} x \cos 6x - \int \left( -\frac{1}{6} \cos 6x \right) dx\)
D. \(6x \cos \frac{1}{6} x + \int \left(6 \cos \frac{1}{6} x \right) dx\)
**Task:**
Evaluate the integral.
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