Example 1.  Numerically approximate the integral  [Graphics:Images/TrapezoidalRuleMod_gr_50.gif]  by using the trapezoidal rule with  m = 1, 2, 4, 8, and 16  subintervals.

Solution 1.

[Graphics:../Images/TrapezoidalRuleMod_gr_51.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_52.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_53.gif]

We will use simulated hand computations for the solution.

 

[Graphics:../Images/TrapezoidalRuleMod_gr_54.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_55.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_56.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_57.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_58.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_59.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_60.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_61.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_62.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_63.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_64.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_65.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_66.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_67.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_68.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_69.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004