Evaluate the definite integral of x^(-1)

Printable View

• Sep 24th 2013, 03:45 PM
dokrbb
Evaluate the definite integral of x^(-1)
I'm just starting calc II and I didn't manage to see a lot of examples, but from the basic information I have got so far I'm confused about this one:

$\displaystyle \int_{-6}^{-3} (x^{-1} + 4x)$ and by evaluating it I get $\displaystyle (ln|x| + 2x^{2})$ that I need to evaluate from -3 to -6 , how do I evaluate the ln|x| for negative numbers, or there is a trick I don't see...

thank you,
• Sep 24th 2013, 03:48 PM
FelixFelicis28
Re: Evaluate the definite integral of x^(-1)
The key here is that the argument of the logarithm is $\displaystyle |x|$, not just $\displaystyle x$.
• Sep 24th 2013, 03:57 PM
dokrbb
Re: Evaluate the definite integral of x^(-1)
Quote:

Originally Posted by FelixFelicis28
The key here is that the argument of the logarithm is $\displaystyle |x|$, not just $\displaystyle x$.

so I can do in this way $\displaystyle ln|x| = ln|-3| = ln3$ ...
• Sep 24th 2013, 05:22 PM
votan
Re: Evaluate the definite integral of x^(-1)
yes