Evaluate the integral. dx 2 (a² + x²)3/21 a>
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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![### Integral Evaluation Problem
**Problem Statement:**
Evaluate the following integral:
\[ 2 \int_{0}^{a} \frac{dx}{(a^2 + x^2)^{3/2}}, \quad a > 0 \]
**Details:**
- The function under the integral is \(\frac{1}{(a^2 + x^2)^{3/2}}\).
- The limits of integration are from 0 to \(a\).
- The given condition is \(a > 0\).
This integral involves evaluating the definite integral of a function which may require techniques such as trigonometric substitution or recognition of a standard integral form.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5abad2ef-7d64-4544-b6f7-dd3dfbff74f8%2Fbeec0503-04ba-4835-a7d8-65992a06df77%2Fzkuhw4s_processed.png&w=3840&q=75)
Transcribed Image Text:### Integral Evaluation Problem
**Problem Statement:**
Evaluate the following integral:
\[ 2 \int_{0}^{a} \frac{dx}{(a^2 + x^2)^{3/2}}, \quad a > 0 \]
**Details:**
- The function under the integral is \(\frac{1}{(a^2 + x^2)^{3/2}}\).
- The limits of integration are from 0 to \(a\).
- The given condition is \(a > 0\).
This integral involves evaluating the definite integral of a function which may require techniques such as trigonometric substitution or recognition of a standard integral form.
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