You have to remember your constant of integration (that + c). The question gives you the one point (1, 7) so that you can calculate that constant.
4t - 2t^3 + c
4(1) - 2(1)^3 + c = 7
c = 5
4t - 2t^3 + 5
A particle moves along the x-axis so that at any time t>0, its velocity is given by . If the particle is at position x=7 at time t=1, what is the position of the particle at time t=2?
How would I figure out the position of the particle when I'm only given the velocity equation and not the position equation? I tried integrating the velocity equation to get the position equation, but when I plug back in t=1, the position equation that I get from integrating doesn't give me x=7.