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Unformatted text preview: 4/10/2011 1 Integration Trapezoidal rule Riemanns integral Simpsons rule Matlab built in functions for integration Lecture 18: Numerical integration Error analysis Integration For a function f , The integral of f from a to b is the area under the graph of the function. If f is continuous, then the area is well defined, as the common limit of upper and lower sums. The integral is denoted If a function g is the primitive of f , namely for all x , then the fundamental theorem of calculus gives that the integral of f can be computed by evaluating g Integration x f x g b But finding primitives can be hard In many cases of engineering and scientific (and economics, etc) interest the functions do not have known primitives, so the integral (area) must be approximated by a finite number of function evaluations. ) ( ) ( ) ( a g b g dx x f a Discretization grid Exactly like in numerical differentiation, one creates a discrete grid on...
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