Find the values of p for which each integral converges. 2 a. 1 dx x(In x)P 2 a. For what values of p will 1 OA. P> OB. P< OC. p= b. ∞ 2 dx x(In x)P dx x(In x)P converge? Select the correct choice below and fill in the answer box to complete your choice.
Find the values of p for which each integral converges. 2 a. 1 dx x(In x)P 2 a. For what values of p will 1 OA. P> OB. P< OC. p= b. ∞ 2 dx x(In x)P dx x(In x)P converge? Select the correct choice below and fill in the answer box to complete your choice.
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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![**Title: Determining Convergence of Integrals**
**Objective:**
Find the values of \( p \) for which each integral converges.
---
**Integrals to Analyze:**
a. \(\int_{1}^{2} \frac{dx}{x(\ln x)^p}\)
b. \(\int_{2}^{\infty} \frac{dx}{x(\ln x)^p}\)
---
**Problem a:**
Determine for what values of \( p \) the integral \(\int_{1}^{2} \frac{dx}{x(\ln x)^p}\) converges. Select the correct choice below and fill in the answer box to complete your choice.
**Choices:**
- A. \( p > \) [ ]
- B. \( p < \) [ ]
- C. \( p = \) [ ]
---
**Instructions:**
Identify the correct condition for \( p \) that ensures convergence of the given integral. Select the appropriate inequality or value and fill in the box provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6851e105-8727-4477-9935-da490bfe86c3%2F7ac80f09-0e17-4d0e-9020-aa30a99271c3%2F5exln34_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Determining Convergence of Integrals**
**Objective:**
Find the values of \( p \) for which each integral converges.
---
**Integrals to Analyze:**
a. \(\int_{1}^{2} \frac{dx}{x(\ln x)^p}\)
b. \(\int_{2}^{\infty} \frac{dx}{x(\ln x)^p}\)
---
**Problem a:**
Determine for what values of \( p \) the integral \(\int_{1}^{2} \frac{dx}{x(\ln x)^p}\) converges. Select the correct choice below and fill in the answer box to complete your choice.
**Choices:**
- A. \( p > \) [ ]
- B. \( p < \) [ ]
- C. \( p = \) [ ]
---
**Instructions:**
Identify the correct condition for \( p \) that ensures convergence of the given integral. Select the appropriate inequality or value and fill in the box provided.
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