This question is taken from Fisher's "Complex Variables 2nd Edition" on page 74.
Is my computation correct? Let me know.
Thanks a lot.
I think there is a much easier parameterisation. If you are going from the point and going to , that means you are trying to find the line between the points (1, 0) and (-1, 1).
The direction vector is , and so your line is .
Therefore your parameterisation is and with . And therefore your line is given by the function .
So evaluating your integral:
Go from here.
As I was using your method, it gave me the right answer and also, showed me where I did wrong on my previous solution (I had (-2i)^2 = -4i, which should be just -4).
Using the result of a theorem to evaluate this is more efficient, but I appreciate all the help man!