16 – x2 dx - Evaluate the integral: 9x?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Evaluate the integral:**
\[
\int \frac{\sqrt{16 - \frac{x^2}{9x^2}}}{9x^2} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \(x = 4 \tan(\theta)\)
- \(x = 4 \sin(\theta)\)
- \(x = 16 \sec(\theta)\)
- \(x = 16 \sin(\theta)\)
- \(x = 4 \sec(\theta)\)
- \(x = 16 \tan(\theta)\)
**(B) Which integral do you obtain after substituting for \(x\) and simplifying?**
*Note: to enter \(\theta\), type the word theta.*
\[
\int \boxed{} \, d\theta
\]
**(C) What is the value of the above integral in terms of \(\theta\)?**
\[
\boxed{} + C
\]
**(D) What is the value of the original integral in terms of \(x\)?**
\[
\boxed{} + C
\]
---
**Question Help:**
[Video]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F284e3ac9-3468-43c5-8292-196f76a9fc38%2F4477723a-4900-4649-803c-4bd24b7da373%2Fzwamgbe_processed.png&w=3840&q=75)
Transcribed Image Text:**Evaluate the integral:**
\[
\int \frac{\sqrt{16 - \frac{x^2}{9x^2}}}{9x^2} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \(x = 4 \tan(\theta)\)
- \(x = 4 \sin(\theta)\)
- \(x = 16 \sec(\theta)\)
- \(x = 16 \sin(\theta)\)
- \(x = 4 \sec(\theta)\)
- \(x = 16 \tan(\theta)\)
**(B) Which integral do you obtain after substituting for \(x\) and simplifying?**
*Note: to enter \(\theta\), type the word theta.*
\[
\int \boxed{} \, d\theta
\]
**(C) What is the value of the above integral in terms of \(\theta\)?**
\[
\boxed{} + C
\]
**(D) What is the value of the original integral in terms of \(x\)?**
\[
\boxed{} + C
\]
---
**Question Help:**
[Video]
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