Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent." Sº 6e *dx
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent." Sº 6e *dx
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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![**Problem Statement:**
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent."
\[
\int_{0}^{\infty} 6e^{-x} \, dx
\]
**Guidance:**
To determine whether the given integral is convergent or divergent, we need to assess the behavior of the function \(6e^{-x}\) as \(x\) approaches infinity. We do this by evaluating the improper integral:
1. Evaluate the indefinite integral of \(6e^{-x}\).
2. Apply the limits of integration from 0 to infinity.
3. Determine the convergence or divergence based on the evaluated result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd3494d7-16cb-4f96-a1a3-f69334a1e65b%2F1133c5fa-6d03-4a24-872c-b6e7fcd487df%2F1vign8_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent."
\[
\int_{0}^{\infty} 6e^{-x} \, dx
\]
**Guidance:**
To determine whether the given integral is convergent or divergent, we need to assess the behavior of the function \(6e^{-x}\) as \(x\) approaches infinity. We do this by evaluating the improper integral:
1. Evaluate the indefinite integral of \(6e^{-x}\).
2. Apply the limits of integration from 0 to infinity.
3. Determine the convergence or divergence based on the evaluated result.
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