Example 11.   Let  [Graphics:Images/Simpson38RuleMod_gr_183.gif]  over  [Graphics:Images/Simpson38RuleMod_gr_184.gif].  Use Simpson's 3/8 rule to approximate the value of the integral.

Solution 11.

[Graphics:../Images/Simpson38RuleMod_gr_185.gif]

[Graphics:../Images/Simpson38RuleMod_gr_186.gif]

m sample points

Simpson38[a,b,m]

4

[Graphics:../Images/Simpson38RuleMod_gr_187.gif]

7

[Graphics:../Images/Simpson38RuleMod_gr_188.gif]

10

[Graphics:../Images/Simpson38RuleMod_gr_189.gif]

13

[Graphics:../Images/Simpson38RuleMod_gr_190.gif]

16

[Graphics:../Images/Simpson38RuleMod_gr_191.gif]

19

[Graphics:../Images/Simpson38RuleMod_gr_192.gif]

25

[Graphics:../Images/Simpson38RuleMod_gr_193.gif]

31

[Graphics:../Images/Simpson38RuleMod_gr_194.gif]

37

[Graphics:../Images/Simpson38RuleMod_gr_195.gif]

43

[Graphics:../Images/Simpson38RuleMod_gr_196.gif]

49

[Graphics:../Images/Simpson38RuleMod_gr_197.gif]

55

[Graphics:../Images/Simpson38RuleMod_gr_198.gif]

61

[Graphics:../Images/Simpson38RuleMod_gr_199.gif]

67

[Graphics:../Images/Simpson38RuleMod_gr_200.gif]

73

[Graphics:../Images/Simpson38RuleMod_gr_201.gif]

79

[Graphics:../Images/Simpson38RuleMod_gr_202.gif]

85

[Graphics:../Images/Simpson38RuleMod_gr_203.gif]

91

[Graphics:../Images/Simpson38RuleMod_gr_204.gif]

106

[Graphics:../Images/Simpson38RuleMod_gr_205.gif]

121

[Graphics:../Images/Simpson38RuleMod_gr_206.gif]

[Graphics:../Images/Simpson38RuleMod_gr_207.gif]

Animation 1.  ( Simpson's 3/8 Rule  Simpson's 3/8 Rule ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004