   Chapter 7.7, Problem 48E

Chapter
Section
Textbook Problem

# Show that if f is a polynomial of degree 3 or lower, then Simpson’s Rule gives the exact value of ∫ a b f ( x ) d x .

To determine

To evaluate: To show that is f(x) is a polynomial of degree 3 or lower, then Simpson’s Rule gives the exact value of abfxdx

Explanation

Formula used:

Error bound for Simpson’s Rule

Mb-a5180 n4

Where M is constant.

Proof: We know that the error bound for Simpson’s Rule using even rectangles to approximate abfxdx is given by:

Mb-a5180 n4

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