Example 11.   Let  [Graphics:Images/BooleRuleMod_gr_181.gif]  over  [Graphics:Images/BooleRuleMod_gr_182.gif].  Use Boole's rule to approximate the value of the integral.

Solution 11.

[Graphics:../Images/BooleRuleMod_gr_183.gif]

[Graphics:../Images/BooleRuleMod_gr_184.gif]

m sample points

Boole[a,b,m]

5

[Graphics:../Images/BooleRuleMod_gr_185.gif]

9

[Graphics:../Images/BooleRuleMod_gr_186.gif]

13

[Graphics:../Images/BooleRuleMod_gr_187.gif]

17

[Graphics:../Images/BooleRuleMod_gr_188.gif]

21

[Graphics:../Images/BooleRuleMod_gr_189.gif]

25

[Graphics:../Images/BooleRuleMod_gr_190.gif]

29

[Graphics:../Images/BooleRuleMod_gr_191.gif]

33

[Graphics:../Images/BooleRuleMod_gr_192.gif]

37

[Graphics:../Images/BooleRuleMod_gr_193.gif]

41

[Graphics:../Images/BooleRuleMod_gr_194.gif]

49

[Graphics:../Images/BooleRuleMod_gr_195.gif]

57

[Graphics:../Images/BooleRuleMod_gr_196.gif]

65

[Graphics:../Images/BooleRuleMod_gr_197.gif]

73

[Graphics:../Images/BooleRuleMod_gr_198.gif]

81

[Graphics:../Images/BooleRuleMod_gr_199.gif]

89

[Graphics:../Images/BooleRuleMod_gr_200.gif]

97

[Graphics:../Images/BooleRuleMod_gr_201.gif]

105

[Graphics:../Images/BooleRuleMod_gr_202.gif]

113

[Graphics:../Images/BooleRuleMod_gr_203.gif]

121

[Graphics:../Images/BooleRuleMod_gr_204.gif]

[Graphics:../Images/BooleRuleMod_gr_205.gif]

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004