Example 6.  Numerically approximate the integral [Graphics:Images/SimpsonRuleMod_gr_126.gif] by using Simpson's rule with  m = 1, 2, 4, and 8.

Solution 6.

We will use simulated hand computations for the solution.

[Graphics:../Images/SimpsonRuleMod_gr_127.gif]

[Graphics:../Images/SimpsonRuleMod_gr_128.gif]

[Graphics:../Images/SimpsonRuleMod_gr_129.gif]

[Graphics:../Images/SimpsonRuleMod_gr_130.gif]
[Graphics:../Images/SimpsonRuleMod_gr_131.gif]
[Graphics:../Images/SimpsonRuleMod_gr_132.gif]


[Graphics:../Images/SimpsonRuleMod_gr_133.gif]
[Graphics:../Images/SimpsonRuleMod_gr_134.gif]
[Graphics:../Images/SimpsonRuleMod_gr_135.gif]


[Graphics:../Images/SimpsonRuleMod_gr_136.gif]
[Graphics:../Images/SimpsonRuleMod_gr_137.gif]
[Graphics:../Images/SimpsonRuleMod_gr_138.gif]


[Graphics:../Images/SimpsonRuleMod_gr_139.gif]
[Graphics:../Images/SimpsonRuleMod_gr_140.gif]
[Graphics:../Images/SimpsonRuleMod_gr_141.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004