Example 11.  Let  [Graphics:Images/MidpointRuleMod_gr_176.gif]  over  [Graphics:Images/MidpointRuleMod_gr_177.gif].  Use the Midpoint Rule to approximate the value of the integral.

Solution 11.

[Graphics:../Images/MidpointRuleMod_gr_178.gif]

[Graphics:../Images/MidpointRuleMod_gr_179.gif]

m sample points

MidpointRule[a,b,m]

1

[Graphics:../Images/MidpointRuleMod_gr_180.gif]

2

[Graphics:../Images/MidpointRuleMod_gr_181.gif]

4

[Graphics:../Images/MidpointRuleMod_gr_182.gif]

6

[Graphics:../Images/MidpointRuleMod_gr_183.gif]

8

[Graphics:../Images/MidpointRuleMod_gr_184.gif]

10

[Graphics:../Images/MidpointRuleMod_gr_185.gif]

12

[Graphics:../Images/MidpointRuleMod_gr_186.gif]

14

[Graphics:../Images/MidpointRuleMod_gr_187.gif]

16

[Graphics:../Images/MidpointRuleMod_gr_188.gif]

20

[Graphics:../Images/MidpointRuleMod_gr_189.gif]

24

[Graphics:../Images/MidpointRuleMod_gr_190.gif]

28

[Graphics:../Images/MidpointRuleMod_gr_191.gif]

32

[Graphics:../Images/MidpointRuleMod_gr_192.gif]

40

[Graphics:../Images/MidpointRuleMod_gr_193.gif]

50

[Graphics:../Images/MidpointRuleMod_gr_194.gif]

60

[Graphics:../Images/MidpointRuleMod_gr_195.gif]

70

[Graphics:../Images/MidpointRuleMod_gr_196.gif]

80

[Graphics:../Images/MidpointRuleMod_gr_197.gif]

100

[Graphics:../Images/MidpointRuleMod_gr_198.gif]

120

[Graphics:../Images/MidpointRuleMod_gr_199.gif]

[Graphics:../Images/MidpointRuleMod_gr_200.gif]

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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004