Example 5.   Let  [Graphics:Images/RiemannSumMod_gr_85.gif]  over  [Graphics:Images/RiemannSumMod_gr_86.gif].  Compare the left Riemann sum, right Riemann sum, midpoint rule and trapezoidal rule for n = 100 subintervals.  Compare them with the analytic solution.  

Solution 5.

[Graphics:../Images/RiemannSumMod_gr_87.gif]




[Graphics:../Images/RiemannSumMod_gr_88.gif]
[Graphics:../Images/RiemannSumMod_gr_89.gif]
[Graphics:../Images/RiemannSumMod_gr_90.gif]
[Graphics:../Images/RiemannSumMod_gr_91.gif]
[Graphics:../Images/RiemannSumMod_gr_92.gif]
[Graphics:../Images/RiemannSumMod_gr_93.gif]
[Graphics:../Images/RiemannSumMod_gr_94.gif]
[Graphics:../Images/RiemannSumMod_gr_95.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004