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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![**Integration Problem with Trigonometric Substitution**
Evaluate the integral:
\[ \int \frac{17}{x^2 \sqrt{x^2 + 25}} \, dx \]
---
**(A) Which trig substitution is correct for this integral?**
- [ ] \( x = 5 \tan(\theta) \)
- [ ] \( x = 17 \sec(\theta) \)
- [ ] \( x = 25 \sin(\theta) \)
- [ ] \( x = 25 \tan(\theta) \)
- [ ] \( x = 25 \sec(\theta) \)
- [ ] \( x = 5 \sin(\theta) \)
---
**(B) Which integral do you obtain after substituting for \( x \) and simplifying?**
**Note:** to enter \( \theta \), type the word "theta."
\[ \int \boxed{\phantom{answer}} \, d\theta \]
---
**(C) What is the value of the above integral in terms of \( \theta \)?**
\[ \boxed{\phantom{answer}} + C \]
---
**(D) What is the value of the original integral in terms of \( x \)?**
\[ \boxed{\phantom{answer}} + C \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc31d976c-acd4-451e-8eb9-fde305025b60%2F9978ba4c-d3eb-42a8-98dd-bc3afba2d52e%2Fbik06sa_processed.png&w=3840&q=75)
Transcribed Image Text:**Integration Problem with Trigonometric Substitution**
Evaluate the integral:
\[ \int \frac{17}{x^2 \sqrt{x^2 + 25}} \, dx \]
---
**(A) Which trig substitution is correct for this integral?**
- [ ] \( x = 5 \tan(\theta) \)
- [ ] \( x = 17 \sec(\theta) \)
- [ ] \( x = 25 \sin(\theta) \)
- [ ] \( x = 25 \tan(\theta) \)
- [ ] \( x = 25 \sec(\theta) \)
- [ ] \( x = 5 \sin(\theta) \)
---
**(B) Which integral do you obtain after substituting for \( x \) and simplifying?**
**Note:** to enter \( \theta \), type the word "theta."
\[ \int \boxed{\phantom{answer}} \, d\theta \]
---
**(C) What is the value of the above integral in terms of \( \theta \)?**
\[ \boxed{\phantom{answer}} + C \]
---
**(D) What is the value of the original integral in terms of \( x \)?**
\[ \boxed{\phantom{answer}} + C \]
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