Consider the parametric curve given by the equations:
How many units of distance are covered by the point P(t) = (x(t),y(t)) between t=0, and t=3 ?
There are few ways to do this problem
1: use the arc length fromula
This gives
Just simplify and integrate and you are done.
2: subtract the equations from each other to get
Note that
Since the above is a line with slope one we can use the pythagorean theorem. So both sides have length 99