MATH 249 Lecture 2: Math 249 L01 Lecture Apr 8
15 Oct 2016
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If f 0 is continuous on [a; b] ; then. F 0 (x) dx = f (b) (cid:0) f (a) : This follows from the fundamental theorem of calculus. Z b a f (x) dx = f (b) (cid:0) f (a) ; since f (x) = f 0 (x) : The rate of change of f The net change in the value of f: a. If s (t) denotes the position of a particle at time t; then velocity v (t) = d dt (s (t)) is the rate of change of position with respect to time. The rate at which position is changing t1. The net change in position over the time interval from t1 to t2: z s (t2) (cid:0) s (t1) Suppose a ball is dropped at a certain height above the ground. The net change theorem implies that the integral of velocity over the time interval.
