f(t) = (4 - t)^(3)
g(t) = t^(3)
h(t) = ((4 - t)^(2) * (-2 + t))
p(t) = (t^(2) * (2 - t))
q(t) = (((4 - t) * (-1 + t)) * (3 - t))
r(t) = ((t * (3 - t)) * (-1 + t))
s(t) = (t * (3 - t)^(2))
w(t) = ((4 - t) * (-1 + t)^(2))
a: 1 / 6
p0(t) = If[0 ≤ t ∧ t < 1, (a * g(t)), 0]
b(x) = x < 0
c(x) = x > 4
p1(t) = If[1 ≤ t ∧ t < 2, (a * (p(t) + w(t) + r(t))), 0]
p2(t) = If[2 ≤ t ∧ t < 3, (a * (q(t) + s(t) + h(t))), 0]
p3(t) = If[3 ≤ t ∧ t < 4, (a * f(t)), 0]