The velocity of an object t seconds after it started moving is t(t-6). Find the total change in the object's position in the 6th second.
v = t^2 - 6 t
x = (1/3)t^3 - 3 t^2 + c
x(6) = (1/3)(36*6) - 3 (36) + c
= 72 - 108 + c = -36 + c
x(5) = (1/3)(125) - 75 + c
= -33.3 + c
x(6)-x(5) = -36 + c +33.3 - c
= - 2 2/3