Parametric Representation for a Contour Integral
Hi, I am having a lot of trouble understanding the concept of "parametric representation" in general. I have the following quiestion,
For the functions f and contours C, use parametric representations for C or legs of C to evaluate the contour integral of f(z)dz.
f(z) is defined by the equations:
1 when y < 0
4y when y >0
and C is the arc from z = -1 - i to z = 1 + i along the curve y = x^3.
I have the solution for this question, but I would much rather understand the intuition into these types of problems. From my vague understanding, (-1 -i) to (1 + i) is where we would like to integrate from and we would like to use y = x^3 to paramertize f(z).
Am I on the right track? Any help would be very much appreciated.