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Trapezoidal Rule of Integration - Numerical Methods - Lecture Slides

Slides, Numerical Methods

Post: April 17th, 2013
Description
The main points are: Trapezoidal Rule of Integration, Process of Measuring Area, Lower Limit of Integration, Basis of Trapezoidal Rule, Newton-Cotes Formula, Linear Polynomial, Derivation of Trapezoidal Rule, Area of Trapezoid
The main points are: Trapezoidal Rule of Integration, Process of Measuring Area, Lower Limit of Integration, Basis of Trapezoidal Rule, Newton-Cotes Formula, Linear Polynomial, Derivation of Trapezoidal Rule, Area of Trapezoid
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Trapezoidal Rule of Integration Docsity.com What is Integration Integration: The process of measuring the area under a function plotted on a graph.  f ( x )dx a b y f(x) I   f ( x )dx a b Where: f(x) is the integrand a= lower limit of integration b= upper limit of integration a b x Docsity.com Basis of Trapezoidal Rule Trapezoidal Rule is based on the Newton-Cotes Formula that states if one can approximate the integrand as an nth order polynomial… I   f ( x )dx a b where f ( x )  fn( x ) and f n ( x )  a0  a1 x  ...  an1 x n1  an x n Docsity.com Basis of Trapezoidal Rule Then the integral of that function is approximated by the integral of that nth order polynomial. b b  f ( x )   fn( x ) a a Trapezoidal Rule assumes n=1, that is, the area under the linear polynomial,  a b f ( a )  f ( b )  ( b  a ) f ( x )dx   2   Docsity.com Derivation of the Trapezoidal Rule Docsity.com Meth..

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