Example 3

Let

x = 1 - t², y = 1,       -1 ≤ t ≤ 1.

As t goes from -1 to 1, the point (x, y) moves from (0,1) to (1,1) and then back along the same line to (0,1) again. The path is shown in Figure 6.3.6.

Figure 6.3.6

The path has length one. However, the point goes along the path twice for a total distance of two. The length formula gives the total distance the point moves.