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Justabeginner
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Homework Statement
Does the following integral converge or diverge?
[itex] \int_{0}^{∞} √t * e^{-t}\, dt [/itex]
Exponential function is not under the square root symbol.
Homework Equations
The Attempt at a Solution
Using the ratio test, I have:
sqrt(t+1)* e^(-{t+1})/[sqrt(t)* e^(-t)] = lim t-> ∞ sqrt(t+1)/(e*sqrt(t)) = 0
0 < 1
Therefore, I think the series is absolutely convergent.
Is this correct, and is the logic and method I used correct? Thank you!
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