Example 11.   Let  [Graphics:Images/SimpsonRuleMod_gr_187.gif]  over  [Graphics:Images/SimpsonRuleMod_gr_188.gif].  Use Simpson's rule to approximate the value of the integral.

Solution 11.

[Graphics:../Images/SimpsonRuleMod_gr_189.gif]

[Graphics:../Images/SimpsonRuleMod_gr_190.gif]

m sample points

Simpson[a,b,m]

2

[Graphics:../Images/SimpsonRuleMod_gr_191.gif]

3

[Graphics:../Images/SimpsonRuleMod_gr_192.gif]

4

[Graphics:../Images/SimpsonRuleMod_gr_193.gif]

5

[Graphics:../Images/SimpsonRuleMod_gr_194.gif]

6

[Graphics:../Images/SimpsonRuleMod_gr_195.gif]

7

[Graphics:../Images/SimpsonRuleMod_gr_196.gif]

9

[Graphics:../Images/SimpsonRuleMod_gr_197.gif]

11

[Graphics:../Images/SimpsonRuleMod_gr_198.gif]

13

[Graphics:../Images/SimpsonRuleMod_gr_199.gif]

15

[Graphics:../Images/SimpsonRuleMod_gr_200.gif]

17

[Graphics:../Images/SimpsonRuleMod_gr_201.gif]

19

[Graphics:../Images/SimpsonRuleMod_gr_202.gif]

21

[Graphics:../Images/SimpsonRuleMod_gr_203.gif]

25

[Graphics:../Images/SimpsonRuleMod_gr_204.gif]

29

[Graphics:../Images/SimpsonRuleMod_gr_205.gif]

33

[Graphics:../Images/SimpsonRuleMod_gr_206.gif]

37

[Graphics:../Images/SimpsonRuleMod_gr_207.gif]

41

[Graphics:../Images/SimpsonRuleMod_gr_208.gif]

51

[Graphics:../Images/SimpsonRuleMod_gr_209.gif]

61

[Graphics:../Images/SimpsonRuleMod_gr_210.gif]

[Graphics:../Images/SimpsonRuleMod_gr_211.gif]

Animation 1.  ( Simpson's Rule  Simpson's Rule ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004