Example 2.  Numerically approximate the integral  [Graphics:Images/MidpointRuleMod_gr_67.gif]  by using the midpoint rule with  m = 50, 100, 200, 400  and 800  subintervals.

Solution 2.

We will use the subroutine for the solution.

[Graphics:../Images/MidpointRuleMod_gr_68.gif]

[Graphics:../Images/MidpointRuleMod_gr_69.gif]
[Graphics:../Images/MidpointRuleMod_gr_70.gif]
[Graphics:../Images/MidpointRuleMod_gr_71.gif]


[Graphics:../Images/MidpointRuleMod_gr_72.gif]
[Graphics:../Images/MidpointRuleMod_gr_73.gif]
[Graphics:../Images/MidpointRuleMod_gr_74.gif]


[Graphics:../Images/MidpointRuleMod_gr_75.gif]
[Graphics:../Images/MidpointRuleMod_gr_76.gif]
[Graphics:../Images/MidpointRuleMod_gr_77.gif]


[Graphics:../Images/MidpointRuleMod_gr_78.gif]
[Graphics:../Images/MidpointRuleMod_gr_79.gif]
[Graphics:../Images/MidpointRuleMod_gr_80.gif]


[Graphics:../Images/MidpointRuleMod_gr_81.gif]
[Graphics:../Images/MidpointRuleMod_gr_82.gif]
[Graphics:../Images/MidpointRuleMod_gr_83.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004