compute the integral of a complex-valued polynomial along a curve

This question is taken from Fisher's "Complex Variables 2nd Edition" on page 74.

Is my computation correct? Let me know.

Thanks a lot.

Re: compute the integral of a complex-valued polynomial along a curve

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.

Re: compute the integral of a complex-valued polynomial along a curve

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!

Re: compute the integral of a complex-valued polynomial along a curve

Just out of interest, which theorem is more efficient in this case?