2 Definition of a Definite Integral If f is a function defined for a s x

Definition of a Definite Integral If f is a function defined fora x b, we divide the interval [a, b] into n subintervals of equal width Ax (b a)/n. We let xo a), 11, x2,. . b) be the endpoints of these subintervals and we be any sample points in these subintervals, so lies in the ith let Xl , & , subinterval [Xi-l, Xi]. Then the definite integral of f from a to b is lim f(xf) Ax provided that this limit exists and gives the same value for all possible choices of sample points. If it does exist, we say that f is integrable on [a, b].