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1. For each of the following improper integrals, determine whether it's convergent or divergent. ∞ (a) dx (Ⓒ) [" (+1) ax dx 1 1 (0) [₁, (x² + 2x) dx - 1 e () [(¹+²) dx x3

1. For each of the following improper integrals, determine whether it's convergent or divergent. ∞ (a) dx (Ⓒ) [" (+1) ax dx 1 1 (0) [₁, (x² + 2x) dx - 1 e () [(¹+²) dx x3

Advanced Engineering Mathematics
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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1. For each of the following improper integrals, determine whether it’s convergent or divergent. (a) \(\int_{1}^{\infty} \left(\frac{\ln x}{x^2}\right) dx\) (b) \(\int_{-1}^{1} \left(\frac{1}{x^2 - 2x}\right) dx\) (c) \(\int_{1}^{\infty} \left(\frac{x^2 + 1}{x^3 + 1}\right) dx\) (d) \(\int_{2}^{\infty} \left(\frac{1 + e^{-x}}{x^3}\right) dx\)
Transcribed Image Text:1. For each of the following improper integrals, determine whether it’s convergent or divergent. (a) \(\int_{1}^{\infty} \left(\frac{\ln x}{x^2}\right) dx\) (b) \(\int_{-1}^{1} \left(\frac{1}{x^2 - 2x}\right) dx\) (c) \(\int_{1}^{\infty} \left(\frac{x^2 + 1}{x^3 + 1}\right) dx\) (d) \(\int_{2}^{\infty} \left(\frac{1 + e^{-x}}{x^3}\right) dx\)
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