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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

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