by the path is y=x
so when t=0 we are at the point (1,1) and when we are at (0,0) we will travel back and forth along this line segment 8 times between 0 and 4pi
the distance between (0,0) and (1,1) is
and we do it 8 times so we get
Or you could do it with an integral, but why? It is too much work.