Show that Simpson's rule is exact for all cubic polynomials and hence using a suitable quartic polynomial obtain the error term in the form Kƒ(iv) (§) (where f(iv) denotes the fourth derivative of f) for some value &€ (-h, h) where K is a constant to be determined. Show that the error in the integral I is consistent with this error term.
Show that Simpson's rule is exact for all cubic polynomials and hence using a suitable quartic polynomial obtain the error term in the form Kƒ(iv) (§) (where f(iv) denotes the fourth derivative of f) for some value &€ (-h, h) where K is a constant to be determined. Show that the error in the integral I is consistent with this error term.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 66E
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