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

1. Feb 12, 2012

### tm5501987

1. The problem statement, all variables and given/known data
The question says use the comparison to determine if $\int_{0}^{1}\frac{e^{-x}}{\sqrt{x}}dx$ converges. What should I compare to?

2. Relevant equations

3. The attempt at a solution

Last edited: Feb 12, 2012
2. Feb 12, 2012

### 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?

3. Feb 12, 2012

### tm5501987

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

4. Feb 12, 2012

### Dick

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

5. Feb 12, 2012

### tm5501987

Got it, thanks