Arc length Formula

L = ∫ ds

Where

ds √ (1+ (dy/dx)² ) dx                                     if y = f(x), a < x < b

ds √ (1+ (dx/dy)² ) dy                                     if x = h(y), c < y < d

Note that there is no limits were put on the integral as the limits will depend on the ds that we are using. By using the first ds will need x limits of integration and by using the second ds will need y limits of integration.

Idea of the arc length formula as a single integral with dissimilar ways to define ds will be suitable when we run across arc lengths in future sections. As well, this ds notation will be a nice notation for the later section as well.