Assume that f (4) is continuous on [0, 1] and that f (k)(x)satisfies

Chapter 7, Problem 4

(choose chapter or problem)

Assume that \(f^{(4)}\)  is continuous on [0,1] and that \(f^{(k)}(x)\) satisfies \(\left|f^{(k)}(x)\right| \leq 1\) on [0, 1], \(k=1,2,3,4\). Find an upper bound on the absolute error that results from approximating the integral of f over  using (a) the midpoint approximation \(M_{10}\); (b) the trapezoidal approximation \(T_{10}\); and (c) Simpson's rule \(S_{10}\).

Equation Transcription:

Text Transcription:

f^(4)

f^(k) (x)

|f^(k) (x)| leq 1

k=1,2,3,4

M_10

T_10

S_10

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