Ski Track for Ski Jump

In order to prepare for the Winter Olympics games, a ski resort is checking its slopes to make sure that they are compatible with Olympics standard. One of the ski tracks for the ski jump can be described using the function r = 100cos2θ meters for 0 ≤ θ ≤ π/2, as shown in the figure. The organizers of the games would like to find out what is the total length of the ski track.

Determine the arc length of the polar curve.

• Use Simpson's Rule to evaluate the integral if necessary.