dx = -/16 – x² + C V16 – x2
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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![The equation displayed is an integral calculus expression:
\[
\int \frac{x}{\sqrt{16-x^2}} \, dx = -\sqrt{16-x^2} + C
\]
This equation represents the integral of the function \( \frac{x}{\sqrt{16-x^2}} \) with respect to \( x \). The result of the integration is \(-\sqrt{16-x^2} + C\), where \( C \) is the constant of integration. The integral involves a substitution technique common in calculus, often related to trigonometric identities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26e7e7c0-322d-4647-9ed4-9f15000cd51e%2F48cbb869-3569-4e9c-979c-07007b8fc9de%2Fw8b9wcb_processed.png&w=3840&q=75)
Transcribed Image Text:The equation displayed is an integral calculus expression:
\[
\int \frac{x}{\sqrt{16-x^2}} \, dx = -\sqrt{16-x^2} + C
\]
This equation represents the integral of the function \( \frac{x}{\sqrt{16-x^2}} \) with respect to \( x \). The result of the integration is \(-\sqrt{16-x^2} + C\), where \( C \) is the constant of integration. The integral involves a substitution technique common in calculus, often related to trigonometric identities.
Transcribed Image Text:Find \(\int \frac{x}{\sqrt{16-x^2}} \, dx\) first using a trigonometric substitution and then using a standard substitution.
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