2 Definition of a Definite Integral If f is a function defined for a S x = b, we divide the interval [a, b] into a subintervals of equal width Ax = (b - a). We let xo (= a), X1, X2. . ...x, (= b) be the endpoints of these subintervals and we let xi , x7, . . .. xi be any sample points in these subintervals, so xy lies in the ith subinterval [x;-1, x;]. Then the definite integral of f from a to b is f(x) dx = lim Ef(xt) Ax 17 ->30 i= 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].1] Use Definition 2 to find an expression for the area under the graph of f as a limit. DO NOT evaluate the limit ipts] f(x)=x+inx, 3x8