Theory and ExamplesProve that the sum S in Simpson’s Rule

Chapter 8, Problem 30E

(choose chapter or problem)

Problem 30E

Theory and Examples

Prove that the sum S in Simpson’s Rule for is a Riemann sum for ƒ continuous on [a, b]. (See Exercise 29.)

Reference: Exercise 29

Prove that the sum T in the Trapezoidal Rule for is a Riemann sum for ƒ continuous on [a, b]. (Hint: Use the Intermediate Value Theorem to show the existence of ck in the subinterval  satisfying