Transcription of Numerical Analysis: Trapezoidal and Simpson's Rule
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Numerical Analysis: Trapezoidal and Simpson's Rule
NumericalAnalysis:Trapezoidaland Simpson sRuleNatasha , PhDNumerical analysis : Trapezoidal andSimpson s RuleNatasha S. Sharma, PhDNumericalAnalysis:Trapezoidaland Simpson sRuleNatasha , PhDMathematical question we are interested innumerically answeringHow to we evaluateI= baf(x)dx?Calculus tells us that if F(x) is the antiderivative of afunctionf(x) on the interval [a,b], thenI= baf(x)dx=F(x)|ba=F(b) F(a).Practically, most integrals cannot be evaluated using thisapproach. For example, 10dx1 +x5has a complicated antiderivative and it easier to adopt anumerical method to approximate this :Trapezoidaland Simpson sRuleNatasha , PhDNumerical Integration: A General FrameworkIf you cannot solve a problem, then replace it with a near-by problem that you can solve!
Numerical Analysis: Trapezoidal and Simpson’s Rule Natasha S. Sharma, PhD General Trapezoidal Rule T n(f) 1 We saw the trapezoidal rule T 1(f) for 2 points a and b. 2 The rule T 2(f) for 3 points involves three equidistant points: a, a+b 2 and b. 3 We observed the improvement in the accuracy of T 2(f) over T 1(f) so inspired by this, we would like to apply this rule to n + 1 …
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