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AP Calculus:

**A function ƒ(t) is given by**

**ƒ(t) = at(cos(t^2)) + b**

a and b are constants.

f(t) is the velocity in ft/min. of an incredibly indecisive high school boy from his lunch table at time t, moving towards his crush sitting on the other side of the cafeteria.

at t = 0 the boy gets up from his table and begins moving at a rate of 2 ft/min, accelerating towards the human of his dreams at 4 ft/min^2.

**What is the distance between the seats of the two potential lovers?**

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