as usual,
s = ∫ √((dx/dt)^2 + (dy/dt)^2) dt
Using the x(t) you provided, dx/dt = 6cost - 6t sint
s = ∫[0,15] √((6cost - 6t sint)^2 + (-15cos(t) + t cos(t) - 1 + sin(t))^2) dt
Part of a cross-country skier's path can be described with the vector function r = <2 + 6t cos(t), (15 − t) (1 sin(t))> for 0 ≤ t ≤ 15 minutes, with x and y measured in meters.
The derivatives of these functions are given by x′(t) = 6 − 2sin(t) and y′(t) = −15cos(t) + t cos(t) − 1 + sin(t).
Find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.
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