√√x² +4x-5 x+2 1 -dx

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The expression shown is a definite integral:

\[
\int_{1}^{4} \frac{\sqrt{x^2 + 4x - 5}}{x + 2} \, dx
\]

This integral represents the area under the curve of the function \(\frac{\sqrt{x^2 + 4x - 5}}{x + 2}\) from \(x = 1\) to \(x = 4\). The function involves a square root in the numerator and a linear polynomial in the denominator. Solving such integrals often involves techniques like substitution or partial fraction decomposition, depending on the complexity of the integrand.
Transcribed Image Text:The expression shown is a definite integral: \[ \int_{1}^{4} \frac{\sqrt{x^2 + 4x - 5}}{x + 2} \, dx \] This integral represents the area under the curve of the function \(\frac{\sqrt{x^2 + 4x - 5}}{x + 2}\) from \(x = 1\) to \(x = 4\). The function involves a square root in the numerator and a linear polynomial in the denominator. Solving such integrals often involves techniques like substitution or partial fraction decomposition, depending on the complexity of the integrand.
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