Consider the following planar curve, which for t ≥ 0, traces out the involute of a circle of radius a.

x = a(cos(t) + t sin(t))

y = a(sin(t) - t cos(t))

(a) Evalute the are length of this plannar curve on [0, b].

(b) Evalute the are length of this planar curve on [-b, b].