Use comparison theorem to determine if \int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}~dx

[tm5501987]

Homework Statement

The question says use the comparison to determine if $\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx$ converges. What should I compare to?

Homework Equations

The Attempt at a Solution

 

[Dick]

Hi tm5501987. Try using [ /tex] with a forward slash and no space. $$\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx$$
$e^{-x}$ is bounded between 1 and 1/e on [0,1], right?

 

[tm5501987]

I am lost, not sure how that gets me to something I can compare to.

 

[Dick]

$\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx \lt \int_{0}^{1}\frac{1}{\sqrt{x}}dx$. Not so?

 

[tm5501987]

Got it, thanks