?When Is Simpson's Rule Exact?(a) Show that if is a polynomial of degree 3 or lower
Chapter 7, Problem 48(choose chapter or problem)
When Is Simpson's Rule Exact?
(a) Show that if is a polynomial of degree 3 or lower, then Simpson's Rule gives the exact value of \(\int_{a}^{b} f(x) d x\).
(b) Find the approximation for \(\int_{0}^{8}\left(x^{3}-6 x^{2}+4 x\right) d x\) and verify that
is the exact value of the integral.
(c) Use the error bound given in (4) to explain why the statement in part (a) must be true.
Equation Transcription:
Text Transcription:
Integral a b f (x) dx
Integral 0 8 (x^3-6^2+4x)dx
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