Example 11.  Let  [Graphics:Images/TrapezoidalRuleMod_gr_197.gif]  over  [Graphics:Images/TrapezoidalRuleMod_gr_198.gif].  Use the Trapezoidal Rule to approximate the value of the integral.

Solution 11.

[Graphics:../Images/TrapezoidalRuleMod_gr_199.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_200.gif]

m sample points

TrapRule[a,b,m]

2

[Graphics:../Images/TrapezoidalRuleMod_gr_201.gif]

3

[Graphics:../Images/TrapezoidalRuleMod_gr_202.gif]

5

[Graphics:../Images/TrapezoidalRuleMod_gr_203.gif]

7

[Graphics:../Images/TrapezoidalRuleMod_gr_204.gif]

9

[Graphics:../Images/TrapezoidalRuleMod_gr_205.gif]

11

[Graphics:../Images/TrapezoidalRuleMod_gr_206.gif]

13

[Graphics:../Images/TrapezoidalRuleMod_gr_207.gif]

15

[Graphics:../Images/TrapezoidalRuleMod_gr_208.gif]

17

[Graphics:../Images/TrapezoidalRuleMod_gr_209.gif]

21

[Graphics:../Images/TrapezoidalRuleMod_gr_210.gif]

25

[Graphics:../Images/TrapezoidalRuleMod_gr_211.gif]

29

[Graphics:../Images/TrapezoidalRuleMod_gr_212.gif]

33

[Graphics:../Images/TrapezoidalRuleMod_gr_213.gif]

41

[Graphics:../Images/TrapezoidalRuleMod_gr_214.gif]

51

[Graphics:../Images/TrapezoidalRuleMod_gr_215.gif]

61

[Graphics:../Images/TrapezoidalRuleMod_gr_216.gif]

71

[Graphics:../Images/TrapezoidalRuleMod_gr_217.gif]

81

[Graphics:../Images/TrapezoidalRuleMod_gr_218.gif]

101

[Graphics:../Images/TrapezoidalRuleMod_gr_219.gif]

121

[Graphics:../Images/TrapezoidalRuleMod_gr_220.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_221.gif]

Animation 1.  ( Trapezoidal Rule  Trapezoidal Rule ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004