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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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