Example 15.  Let  [Graphics:Images/RiemannSumMod_gr_305.gif]  over  [Graphics:Images/RiemannSumMod_gr_306.gif].  Use the Trapezoidal Rule to approximate the value of the integral.

Solution 15.

[Graphics:../Images/RiemannSumMod_gr_307.gif]


[Graphics:../Images/RiemannSumMod_gr_308.gif]

m sample points

TrapezoidalRule[a,b,m]

2

[Graphics:../Images/RiemannSumMod_gr_309.gif]

3

[Graphics:../Images/RiemannSumMod_gr_310.gif]

5

[Graphics:../Images/RiemannSumMod_gr_311.gif]

7

[Graphics:../Images/RiemannSumMod_gr_312.gif]

9

[Graphics:../Images/RiemannSumMod_gr_313.gif]

11

[Graphics:../Images/RiemannSumMod_gr_314.gif]

13

[Graphics:../Images/RiemannSumMod_gr_315.gif]

15

[Graphics:../Images/RiemannSumMod_gr_316.gif]

17

[Graphics:../Images/RiemannSumMod_gr_317.gif]

21

[Graphics:../Images/RiemannSumMod_gr_318.gif]

25

[Graphics:../Images/RiemannSumMod_gr_319.gif]

29

[Graphics:../Images/RiemannSumMod_gr_320.gif]

33

[Graphics:../Images/RiemannSumMod_gr_321.gif]

41

[Graphics:../Images/RiemannSumMod_gr_322.gif]

51

[Graphics:../Images/RiemannSumMod_gr_323.gif]

61

[Graphics:../Images/RiemannSumMod_gr_324.gif]

71

[Graphics:../Images/RiemannSumMod_gr_325.gif]

81

[Graphics:../Images/RiemannSumMod_gr_326.gif]

101

[Graphics:../Images/RiemannSumMod_gr_327.gif]

121

[Graphics:../Images/RiemannSumMod_gr_328.gif]

[Graphics:../Images/RiemannSumMod_gr_329.gif]

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004