Example 7.  Numerically approximate the integral [Graphics:Images/MidpointRuleMod_gr_131.gif] by using the midpoint rule with  m = 50, 100, 200, 400  and 800  subintervals.

Solution 7.

We will use the subroutine for the solution.

[Graphics:../Images/MidpointRuleMod_gr_132.gif]

[Graphics:../Images/MidpointRuleMod_gr_133.gif]
[Graphics:../Images/MidpointRuleMod_gr_134.gif]
[Graphics:../Images/MidpointRuleMod_gr_135.gif]


[Graphics:../Images/MidpointRuleMod_gr_136.gif]
[Graphics:../Images/MidpointRuleMod_gr_137.gif]
[Graphics:../Images/MidpointRuleMod_gr_138.gif]


[Graphics:../Images/MidpointRuleMod_gr_139.gif]
[Graphics:../Images/MidpointRuleMod_gr_140.gif]
[Graphics:../Images/MidpointRuleMod_gr_141.gif]


[Graphics:../Images/MidpointRuleMod_gr_142.gif]
[Graphics:../Images/MidpointRuleMod_gr_143.gif]
[Graphics:../Images/MidpointRuleMod_gr_144.gif]


[Graphics:../Images/MidpointRuleMod_gr_145.gif]
[Graphics:../Images/MidpointRuleMod_gr_146.gif]
[Graphics:../Images/MidpointRuleMod_gr_147.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004