Example 3.   Let  [Graphics:Images/RiemannSumMod_gr_51.gif]  over  [Graphics:Images/RiemannSumMod_gr_52.gif].  Use the midpoint rule with  n = 25, 50, and 100  to approximate the value of the integral.

Solution 3.

[Graphics:../Images/RiemannSumMod_gr_53.gif]

[Graphics:../Images/RiemannSumMod_gr_54.gif]

[Graphics:../Images/RiemannSumMod_gr_55.gif]
[Graphics:../Images/RiemannSumMod_gr_56.gif]
[Graphics:../Images/RiemannSumMod_gr_57.gif]



[Graphics:../Images/RiemannSumMod_gr_58.gif]

[Graphics:../Images/RiemannSumMod_gr_59.gif]

[Graphics:../Images/RiemannSumMod_gr_60.gif]
[Graphics:../Images/RiemannSumMod_gr_61.gif]
[Graphics:../Images/RiemannSumMod_gr_62.gif]



[Graphics:../Images/RiemannSumMod_gr_63.gif]

[Graphics:../Images/RiemannSumMod_gr_64.gif]

[Graphics:../Images/RiemannSumMod_gr_65.gif]
[Graphics:../Images/RiemannSumMod_gr_66.gif]
[Graphics:../Images/RiemannSumMod_gr_67.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004