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Help! I'm preparing for Prelims (exams taken at the end of the first year of my course in Physics) and I can't do the line integral of (z^2)dz around the open semi-circle counter-clockwise from x=1 to x=-1. However I try to tackle it the answer comes out as 0, when I know it has some size because it cancels out with the straight line integral from -1 to 1 (possibly equal to 2/3, although I've lost the original working). The z is for a complex variable, but if anyone could at least just show me how to parameterize the regular line integral (not for complex, but just in 2D) around the semi-circle that would be so helpful. I've tried everyway I can (barring using cartesian, because I know there's a nice polar way to do it, I just keep coming out 0 when I try though), and it just won't work!
To re-iterate, the integral is (z^2)dz where z = x + iy.
Thank you!
Simon.
To re-iterate, the integral is (z^2)dz where z = x + iy.
Thank you!
Simon.