Exact Simpson's Rule a. Use Simpson's Rule to approximate fóx³ dx using two subin- tervals (n = 2); compare the approximation to the value of the integral. b. Use Simpson's Rule to approximate fóx³ dx using four subin- tervals (n = 4); compare the approximation to the value of the integral. c. Use the error bound associated with Simpson's Rule given in Theorem 8.1 to explain why the approximations in parts (a) and (b) give the exact value of the integral. d. Use Theorem 8.1 to explain why a Simpson's Rule approxi- mation using any (even) number of subintervals gives the exact value of f(x) dx, where f(x) is a polynomial of degree 3 or less.

Exact Simpson's Rule a. Use Simpson's Rule to approximate fóx³ dx using two subin- tervals (n = 2); compare the approximation to the value of the integral. b. Use Simpson's Rule to approximate fóx³ dx using four subin- tervals (n = 4); compare the approximation to the value of the integral. c. Use the error bound associated with Simpson's Rule given in Theorem 8.1 to explain why the approximations in parts (a) and (b) give the exact value of the integral. d. Use Theorem 8.1 to explain why a Simpson's Rule approxi- mation using any (even) number of subintervals gives the exact value of f(x) dx, where f(x) is a polynomial of degree 3 or less.

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 44AR: Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places...

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