Recall that when a curve is given in polar coordinates r = f(θ) for a ≤ θ ≤ b, the arc length of a polar curve is determined as follows:

For the given function r = 100cos2θ for 0 ≤ θ ≤ π/2, the derivative dr/dθ is given by

The arc length of the ski track is determined as:

Since there is no obvious technique to perform the integration, Simpson's Rule is used. According to the Simpson's Rule, an integration can be approximated as,

where n is even and Δθ = (b - a)/n.

In this case, , n = 10, and Δθ = (π/2)/10 = π/20.

The values of f(θ) subject to different values of θ are summarized in the table on the left.

The integration can then be evaluated to give the length of the ski track as