Question

If dx/dt=(t-3)^2 and x=7 when t=0, find x when t=4.

Answer = 49/3
Thanks for anyone's help

Answer 1

dx/dt = t^2 - 6 t + 9

so
x = (1/3) t^3 - 3 t^2 + 9 t + constant
x(0) = 7 = constant
x = (1/3) t^3 - 3 t^2 + 9 t + 7
put in t = 4