# Determining Convergence/Divergence

1. Mar 25, 2008

### silicon_hobo

1. The problem statement, all variables and given/known data
Determine whether each integral is convergent or divergent, if convergent find its value.
a)$$\int^2_1 \frac{dx}{x \ ln \ x}$$

b)$$\int^3_0 (\frac{1}{\sqrt{x}})e^{-\sqrt{x}}\ dx$$

3. The attempt at a solution
Hey Folks, I'm still at it. Both of these integrals have discontinuities at the left endpoint. I've completed the integration and applied the appropriate equation. However, I'm not sure how to interpret the results.

In this one ln(ln(1)) does not exist. Does that mean I should stop there and declare the inetgral divergent?

There are no terms here that cannot be calculated but again I am getting a negative answer. Does this signify divergence? Thank you for clearing this up!

Last edited: Mar 26, 2008
2. Mar 26, 2008

### HallsofIvy

Staff Emeritus
You've lost a sign:
$$\int e^{-u} du= -e^{-u}+ C$$