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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