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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