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**darleneflorio** A particle moves along the x-axis so that its velocity at time t is given by v(t)=-(t+1)sin(t^2/2). During the time interval 0<t<3 or equal to t, what is the total distance between the particle and the origin? At t = 0 , the particle is at position x = 1.

The answer is x(0)+ antideriviative of v(t) from 0 to the square of 2pi.

Please explain why.

x(0) must be where you start from and the total distance traveled is 4.334. But I'm still confused on why the distance is 2.265.