Example 14.  Let  [Graphics:Images/RiemannSumMod_gr_280.gif]  over  [Graphics:Images/RiemannSumMod_gr_281.gif].  Use the Midpoint Rule to approximate the value of the integral.

Solution 14.

[Graphics:../Images/RiemannSumMod_gr_282.gif]


[Graphics:../Images/RiemannSumMod_gr_283.gif]

m sample points

MidPointRule[a,b,m]

1

[Graphics:../Images/RiemannSumMod_gr_284.gif]

2

[Graphics:../Images/RiemannSumMod_gr_285.gif]

4

[Graphics:../Images/RiemannSumMod_gr_286.gif]

6

[Graphics:../Images/RiemannSumMod_gr_287.gif]

8

[Graphics:../Images/RiemannSumMod_gr_288.gif]

10

[Graphics:../Images/RiemannSumMod_gr_289.gif]

12

[Graphics:../Images/RiemannSumMod_gr_290.gif]

14

[Graphics:../Images/RiemannSumMod_gr_291.gif]

16

[Graphics:../Images/RiemannSumMod_gr_292.gif]

20

[Graphics:../Images/RiemannSumMod_gr_293.gif]

24

[Graphics:../Images/RiemannSumMod_gr_294.gif]

28

[Graphics:../Images/RiemannSumMod_gr_295.gif]

32

[Graphics:../Images/RiemannSumMod_gr_296.gif]

40

[Graphics:../Images/RiemannSumMod_gr_297.gif]

50

[Graphics:../Images/RiemannSumMod_gr_298.gif]

60

[Graphics:../Images/RiemannSumMod_gr_299.gif]

70

[Graphics:../Images/RiemannSumMod_gr_300.gif]

80

[Graphics:../Images/RiemannSumMod_gr_301.gif]

100

[Graphics:../Images/RiemannSumMod_gr_302.gif]

120

[Graphics:../Images/RiemannSumMod_gr_303.gif]

[Graphics:../Images/RiemannSumMod_gr_304.gif]

Animation 5.  ( Midpoint Rule  Midpoint Rule ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004