Ellipse arc length

I had to compute the length of arcs of Earth's meridian. I noticed that there was no analytical solution for this so I wrote this very simple function.

It computes the arc length of an ellipse centered on (0,0) with radius a (along OX) and radius b (along OY)

x(t) = a.cos(t)
y(t) = b.sin(t)

with angle t (in radians) between t1 and t2.

The solution is obtained numerically by dividing the arc in small straight segments. In addition, the second output is the length of the complete ellipse compyted with an approximated formula (Ramanujan).

Luc