Problem 2 (Length is independent of parameterization) To illustrate that the length of a smooth curve in space does not depend on the used parameterization, calculate the length of one turn of the helix 7(t) = (cos t, sin t, t), t ∈ [0, 2π], using the following parameterizations. Show the explicit calculation for all four length integrals. a) r(t) = (cos t, sin t, -t), t ∈ [-2π, 0]. b) r(t) = (cos t^2, sin t^2, 4t^2), t ∈ [0, √(27)]. c) r(t) = (cos 4t, sin 2t, 6t), t ∈ [0, π/2]. d) 7(t) = (cos(e'), sin(e'), e'), t ∈ (-∞, ln(2π)].