Parametrizing a Line Integral: Finding the Easiest Approach

[hawaiifiver]

How do you work out the parameterization for a line integral. I have this example, and the closed curve C bounds the lines y=0, x=2 and y^2 = 8x. In the solution to the problem it states that there are many parameterizations available. So I just wanted to know, how do you work out the parameterization?

 

[CompuChip]

The easiest way is to parametrize each part separately.
The "many parametrizations" probably refers to the fact that you can choose many different "velocities", e.g.
x(t) = (t, 0) ($0 \le t \le 1$)
x(t) = (2t, 0) ($0 \le t \le 1/2$)
x(t) = (t², 0) ($0 \le t \le 1$)
x(t) = (t/2, 0) ($0 \le t \le 2$)
x(t) = (1 - t, 0) ($0 \le t \le 1$)
all parametrize the line segment between (0, 0) and (1, 0) (although the direction of the latter is reversed).