# Simpson's rule

Is the simpson's rule always more accurate than the midpoint rule and trapezoidal rule?

Not always; it is possible that the midpoint and/or trapezoidal rule determine exact values.

1. Some functions values for a function f are given below.

x 0 0.5 1.0
f(x) 3 4 11

What is the value of the estimate S1 to
1
�çf (x) dx
0

(a) 6 b) 5 c) 15/2 (d) 22/3

2. Some functions values for a function f are given below.
x 0 0.5 1.0 1.5 2.0
f(x) 3 4 11 20 30
With these values only which of the following estimates to
2
�çf (x) dx is it possible to
0
calculate?
(a) S1 and S2 only (b) S1 only
(c) S1, S2 and S4 (d) It isn�ft possible to calculate any
Simpson�fs Rule estimates.

3. Some functions values for a function f are given below.
x 11 13 15
f(x) 0.5 a 1.5
If the value of the S1 approximation to
15
�ç f (x) dx is 4, what is the value of
11
a?
(a) 1.5 (b) 1.75
(c) 1.25 (d) 1

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