Example 11.   Let  [Graphics:Images/RiemannSumMod_gr_201.gif]  over  [Graphics:Images/RiemannSumMod_gr_202.gif].  Use the Right Riemann Sum to approximate the value of the integral.

Solution 11.

[Graphics:../Images/RiemannSumMod_gr_203.gif]


[Graphics:../Images/RiemannSumMod_gr_204.gif]

m sample points

RightRiemannSum[a,b,m]

1

[Graphics:../Images/RiemannSumMod_gr_205.gif]

2

[Graphics:../Images/RiemannSumMod_gr_206.gif]

4

[Graphics:../Images/RiemannSumMod_gr_207.gif]

6

[Graphics:../Images/RiemannSumMod_gr_208.gif]

8

[Graphics:../Images/RiemannSumMod_gr_209.gif]

10

[Graphics:../Images/RiemannSumMod_gr_210.gif]

12

[Graphics:../Images/RiemannSumMod_gr_211.gif]

14

[Graphics:../Images/RiemannSumMod_gr_212.gif]

16

[Graphics:../Images/RiemannSumMod_gr_213.gif]

20

[Graphics:../Images/RiemannSumMod_gr_214.gif]

24

[Graphics:../Images/RiemannSumMod_gr_215.gif]

28

[Graphics:../Images/RiemannSumMod_gr_216.gif]

32

[Graphics:../Images/RiemannSumMod_gr_217.gif]

40

[Graphics:../Images/RiemannSumMod_gr_218.gif]

50

[Graphics:../Images/RiemannSumMod_gr_219.gif]

60

[Graphics:../Images/RiemannSumMod_gr_220.gif]

70

[Graphics:../Images/RiemannSumMod_gr_221.gif]

80

[Graphics:../Images/RiemannSumMod_gr_222.gif]

100

[Graphics:../Images/RiemannSumMod_gr_223.gif]

120

[Graphics:../Images/RiemannSumMod_gr_224.gif]

[Graphics:../Images/RiemannSumMod_gr_225.gif]

Animation 2.  ( Right Riemann Sum  Right Riemann Sum ).  Internet hyperlink.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004