MATH 1552 Lecture Notes - Lecture 1: Numerical Integration, Antiderivative

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Sometimes cannot explicitly calculate the area under a graph (integral), because don"t know an anti-derivative, but need to know numerical value good approximations. Let us assume that f is continuous on [a, b] and that we want to get an approximate value for. F (x) dx from a to b. We subdivide the interval [a, b] into n equal intervals of length (b a)/n. So we choose equally spaced partition points a = x0 < x1 < x2 < < xn = b where each interval [xi 1, xi] has length. X = xi xi 1 = (b a)/n mesh size. And let yi = f (xi) , i = 0, 1, 2, , n. Approximate the area under the graph of f from xi 1 to xi: approximate. F (x) dx from xi 1 to xi. Trapezoid = combination of a rectangle and a triangle simply add the areas.

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