Suppose you have the integral:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int^b_{-a}\frac{dx}{x+i\epsilon} [/tex]

where epsilon is a tiny positive number. The integral should be a log shouldn't it?

[tex]=log[b+i\epsilon]-log[-a+i\epsilon]=log-(log[a]+...)[/tex]

where the ... is 'i' times the angle of the point -a+iε. Doesn't this depend on where you put your branch cut? If your cut goes in the direction of the positive imaginary axis, then the angle is -pi (the angle goes from 0 in the direction of the positive real axis, to pi/2, then it drops discontinuously to -3pi/2 as it crosses the cut). However, if you put your cut on the negative real axis, then the angle is +pi. If you put your cut on the positive real axis, the angle is also +pi.

How do you know which cut to use?

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# Integral of 1/z=log(z), which branch?

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