Calculus Question help

Question

A particle moves along a line with velocity v(t) = cos(6πt) for 0 ≤ t ≤ 4.

a) Find the displacement.

b) Find the distance traveled

Answer 1

a)Displacement S = ∫₀²cos(2πt)dt = 1/2πsin(2πt)₀² = 1/2π(sin(4π) - sin(0)) = 0;

b) Distance D = ∫₀²abs(cos(2πt))dt = 8∫₀^1/4cos(2πt)dt = 8/2πsin(2πt)₀^1/4 =4/π(sin(π/2) - sin(0)) = 4/π ≈ 1.273