Can anyone explain the difference between the arc length and total distance? I'm using the textbook here and they seem to be the same formula. Please help me figure this out.
2026-04-02 06:13:57.1775110437
Parametrics Arc Length
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Yes, it is the same formula.
If a particle travel from a point $A$ to a point $B$ along a trajectory described by parametric functions $(x(t),y(t))$, than the ''total distance'' ( I prefer the term ''total path'') is the length of the arc $AB$, and the derivative in the formula of the arc length are the components of the velocity.