MATH 2B Lecture 3: Definite Integrals
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Math 2b - lecture 3 - definite integrals. Suppose that f is a function defined on an interval [a,b]. Let n be a positive integer, define b a x = n and let xi = a + i. = a + n i, for each i. A riemann sum is any expression of the form. We say that the function f is riemann integrable on [a,b] if lim n f (x ) x i converges to the same value for every choice of sample points. In such a case the definite integral of f from a to b is: n i=1 n i=1 f (x ) x i b a f (x)dx. = lim n n i=1 f (x ) x i. If f is continuous on [a,b], or has only a finite number of jump discontinuities, then f is riemann integrable on [a,b] (x)dx. = area under the curve y = f (x) (x)dx.
