v(t) is the integral of a(t), so v(t)=-12 cos(t) + 7 sin(t) +c (where c is a constant)
s(t) is the integral of v(t), so s(t) = -12 sin(t) - 7 cos(t) + ct + d (where d is a constant)
Solving s(0) = 0 gives d = 7.
Solving s(2pi) = 18 gives c = 9/pi.
So the position is s(t) = -12 sin(t) - 7 cos(t) + 9t/pi + 7.
