# Evaluating this definite integral

• Feb 17th 2009, 03:36 PM
fattydq
Evaluating this definite integral
It's the integral from 1 to 10 of x divided by x^2-4. I'm assuming u would be x^2-4 making du 2x so du/2 would be x. Then would I just be left with 1/2 the integral of 1/u and would have to solve it from there?
• Feb 17th 2009, 03:38 PM
Jester
Quote:

Originally Posted by fattydq
It's the integral from 1 to 10 of x divided by x^2-4. I'm assuming u would be x^2-4 making du 2x so du/2 would be x. Then would I just be left with 1/2 the integral of 1/u and would have to solve it from there?

$\displaystyle \int_1^{10} \frac{x}{x^2-4}\,dx$

then you have a problem at -2 and 2! Your integral is improper!
• Feb 17th 2009, 03:41 PM
fattydq
(Doh)
Quote:

Originally Posted by danny arrigo
$\displaystyle \int_1^{10} \frac{x}{x^2-4}\,dx$
You're learning how to evaluate definite integrals, but you can't do this one because the function ain't continuous at $\displaystyle x=2.$ Regarding those bounds, we have $\displaystyle 1\le x\le10$ and $\displaystyle 2$ belongs there.
If the question does not include the $\displaystyle -2$ neither $\displaystyle 2,$ then you can evaluate the integral.