Asked by Randall

Hi,
I have this question here that I'm not sure about.
Any help is appreciated. Evaluate the integral from 1 to 3 of dx/(x-2). This seems like it should be really simple- is it 0?

Answers

Answered by Steve
∫dx/(x-2) = ln(x-2)

first off, ln(x-2) is not defined for x < 2. So, some like to evaluate it as

∫[1,3] dx/(x-2) = ln|x-2| [1,3] = ln|3-2|-ln|1-2| = ln1 - ln1 = 0-0 = 0

That is because the graph is symmetric about (1,0) so the upper and lower areas cancel out.

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