A particle moves such that its velocity at time t is given by
v =5t^5i + 4t^5j + t^3k.
If its position x at time t = 0 is given by x ( 0 ) = i + 2j, what is the position of the particle at time t?
x=INT v(t)dt
=5/6*t^6 i + 4/6 t^6 j + 1/4*t^4k+C
given t=0 x=i+2J
i+2j=i(5/6(0)+2/3 (0)j+Ok+C
C=i+2j