Aparticle moving along the x axis has the position x(t) at time t with the velocity of the particle given by v(t)=5sin(t^2). at time t=6, the particles position is (4,0). find the position of the particle when t=

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V(t) = dx/dt, so x(t) = x(0) + integral 5 sin(t^2) dt. 

But this integral is given by the Fresnel integral, which is a special function. Evaluating numerically, and using the fact that x(6) = 4 gives x(7) = 3.8371.

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