Evaluate the integral: Or= (A) Which trig substitution is correct for this integral? 2 Ox= 5 sec (0) Ox= Ox= Ox= 5 2 sin(0) 25 4 1 -sec (0) -sec(0) √4x² - 25 x³ 4 5 2 sec (0) dx (B) Which integral do you obtain after substituting for a Note: to enter 8, type the word theta. de (C) What is the value of the above integral in terms of 0? +C (D) What is the value of the original integral in terms of x? Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below. +C
Evaluate the integral: Or= (A) Which trig substitution is correct for this integral? 2 Ox= 5 sec (0) Ox= Ox= Ox= 5 2 sin(0) 25 4 1 -sec (0) -sec(0) √4x² - 25 x³ 4 5 2 sec (0) dx (B) Which integral do you obtain after substituting for a Note: to enter 8, type the word theta. de (C) What is the value of the above integral in terms of 0? +C (D) What is the value of the original integral in terms of x? Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below. +C
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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![**Evaluate the integral:**
\[
\int \frac{\sqrt{4x^2 - 25}}{x^3} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \( x = \frac{2}{5} \sec(\theta) \)
- \( x = \frac{5}{2} \sin(\theta) \)
- \( x = \frac{25}{4} \sec(\theta) \)
- \( x = \frac{1}{4} \sec(\theta) \)
- \( x = \frac{5}{2} \sec(\theta) \)
**(B) Which integral do you obtain after substituting for \( x \)?**
*Note: to enter \( \theta \), type the word theta.*
\[ \int \text{\_\_\_} \, d\theta \]
**(C) What is the value of the above integral in terms of \( \theta \)?**
\_\_\_ + \( C \)
**(D) What is the value of the original integral in terms of \( x \)?**
*Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below.*
\_\_\_ + \( C \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb47bac88-cba5-40e5-9f3f-db7316eb95a3%2F1351cf72-58ec-4309-825d-98669524ba77%2F4osqvzs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the integral:**
\[
\int \frac{\sqrt{4x^2 - 25}}{x^3} \, dx
\]
**(A) Which trig substitution is correct for this integral?**
- \( x = \frac{2}{5} \sec(\theta) \)
- \( x = \frac{5}{2} \sin(\theta) \)
- \( x = \frac{25}{4} \sec(\theta) \)
- \( x = \frac{1}{4} \sec(\theta) \)
- \( x = \frac{5}{2} \sec(\theta) \)
**(B) Which integral do you obtain after substituting for \( x \)?**
*Note: to enter \( \theta \), type the word theta.*
\[ \int \text{\_\_\_} \, d\theta \]
**(C) What is the value of the above integral in terms of \( \theta \)?**
\_\_\_ + \( C \)
**(D) What is the value of the original integral in terms of \( x \)?**
*Note: WAMAP does not recognize the inverse secant (arcsec) function. You will need to use another inverse trig function when you fill in your answer below.*
\_\_\_ + \( C \)
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