In this discussion you will consider the Net Change Theorem, in regards to volume and distance. First think of the definite integral of the rate of change of a quantity F'(x), then the definite integral of F'(x) from a to b gives the total change or net change of F(x) on the interval [a, b]' fab F'(x)dx = F(b) F(a) It says that when a quantity changes, the new value equals the initial value plus the integral of the rate of change of that quantity. Net change can be applied to area, distance, and volume, to name only a few applications. Net change accounts for negative quantities automatically without having to write more than one integral. - Use the Net Change Theorem to determine how much water flows into a tank over the first 10 minutes if the water is flowing into the take at a rate of r(t):t2 ft3/minute . Create and solve your own Net Change Theorem problem using total distance by examining the velocity of an object moving along a straight line, where s(t) is the position at time t, and its velocity is v(t) : s'(t) and fa\" u(t)dt = s(b) s(a)