Summation of Series Using Definite Integral as the Limit of a Sum

∫f(x)dx (from a to b) = lim (h→0) h[f(a)+f(a+h)+f(a+2h)+...+f(a+(n-1)h)] where h = (b-a)/n

h→0 implies n→∞



∫f(x)dx (from 0 to 1) = lim (n→∞) (1/n)[Σf(r/n)(from r = to n-1)]