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Lecture8 - Numerical Integration and Differentiation...

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Numerical Integration and Differentiation EGN5455 Lecture 8
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Numerical Integration: Trapezoid rule Objective: to approximate the integral on a given interval [a,b]. Assumption: f(x) is a scalar-valued function of x and has a continuous second derivative. To find the linear polynomial which interpolates (a,f(a)) and (b,f(b)), we can use L i l i Lagrange interpolation: b a x b f b b x a f ) )( ( ) )( ( a a
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Trapezoid rule We integrate the Lagrange polynomial from a to b, with the result: ). ( ) ( ) ( 2 1 a b b f a f Example1: Use the trapezoid rule to approximate the integral of f(x)=x 2 on interval [1,2].  5 . 2 1 2 ) 2 ( ) 1 ( 2 / 1 f f The actual value is 7/3= 2.33
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