Originally Posted by

**kaelbu** I was studying for my multi-variable calculus test, when I realized that their seem to be two very similar ways to calculate the length.

$\displaystyle \int_a^b \sqrt{(dx/dt)^2+ (dy/dt)^2} dt $ (used to calculate arc length) vs $\displaystyle \sqrt{x^2(t)+y^2(t)}$ (used to calculate length of normal vector/ any vector)

And I guess they really are basically the same, but I was wondering if someone could explain the difference, and perhaps why the first one is used in line integrals whereas you use the second in surface integrals.

Thanks!