Example 6.  Numerically approximate the integral [Graphics:Images/TrapezoidalRuleMod_gr_115.gif] by using the trapezoidal rule with  m = 1, 2, 4, 8, and 16  subintervals.

Solution 6.

[Graphics:../Images/TrapezoidalRuleMod_gr_116.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_117.gif]

[Graphics:../Images/TrapezoidalRuleMod_gr_118.gif]

We will use simulated hand computations for the solution.

 

[Graphics:../Images/TrapezoidalRuleMod_gr_119.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_120.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_121.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_122.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_123.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_124.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_125.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_126.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_127.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_128.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_129.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_130.gif]


[Graphics:../Images/TrapezoidalRuleMod_gr_131.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_132.gif]
[Graphics:../Images/TrapezoidalRuleMod_gr_133.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004