Apply Simpson's Rule with n = 2 to approximate I =dx. What is the ...

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Question 1

The following table gives values of an unknown function  f(x)  determined by experimental measurement. Find the best  Simpson's Rule  approximation you can for dx based on the values given in the table.

x	f(x)
2.00	1.052
2.25	1.042
2.50	1.034
2.75	1.026
3.00	1.020
3.25	1.016
3.50	1.012
3.75	1.010
4.00	1.008

◦ S₈  ≈  2.0480
◦ S₈  ≈  2.0473
◦ S₈  ≈  2.0468
◦ S₈  ≈  2.0465
◦ S₈  ≈  2.0477

Question 2

Apply Simpson's Rule with n = 2 to approximate  I  =dx. What is the actual error in this approximation? What does the Simpson's Rule error estimate give as an upper bound for the size of the error?
◦ S₂ = ,  I - S₂ = - ,  estimate gives   ≤
◦ S₂ = ,  I - S₂ = - ,  estimate gives   ≤
◦ S₂ = ,  I - S₂ = ,  estimate gives   ≤
◦ S₂ = ,  I - S₂ = - ,  estimate gives   ≤
◦ S₂ = ,  I - S₂ = 0,  estimate gives   ≤

[Kjones0604]

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Wow, this really help

[patma1981]

Great answer, keep it coming