In this question you will prove that Simpson's Rule is a perfect approximation for cubic polynomials. To do this we will consider the definite integral: 4 fax³ + bx² + cx+d dx with a, b, c, d constants. 0 (a) Write down and evaluate Simpson's Rule with 4 partitions to estimate this integral. (Your final answer here should be in terms of a, b, c, d) (b) Directly evaluate this definite integral and confirm that what you find matches what you found in (a).

In this question you will prove that Simpson's Rule is a perfect approximation for cubic polynomials. To do this we will consider the definite integral: 4 fax³ + bx² + cx+d dx with a, b, c, d constants. 0 (a) Write down and evaluate Simpson's Rule with 4 partitions to estimate this integral. (Your final answer here should be in terms of a, b, c, d) (b) Directly evaluate this definite integral and confirm that what you find matches what you found in (a).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 67E

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