Differential Equation Involving Natural Log.

  • Thread starter theRukus
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  • #1
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Homework Statement


Calculate the following:
[itex]\int^{-4}_{-6} (x^-1+5x)dx[/itex]


Homework Equations





The Attempt at a Solution


I've worked this down to
[itex]ln(-4) + 5(-4) - ln(-6) - 5(-6)
=ln(-4)-ln(-6)+10[/itex]
The answer to the left half (the ln parts) of the equation is undefined, and the right is 10..
So... undefined + 10? I'm unsure what to say the definite answer is....

Thank you for any help.
 

Answers and Replies

  • #2
LCKurtz
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The antiderivative is

[tex]\int \frac 1 x\,dx = \ln |x|+C[/tex]

The absolute value signs matter when x < 0.
 

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