Example 7.  Show that the degree of precision of  Boole's Rule is  [Graphics:Images/NewtonCotesMod_gr_213.gif].  

Solution 7.

It will suffice to apply Boole's rule over the interval  [0,4]  with the seven test functions  [Graphics:../Images/NewtonCotesMod_gr_214.gif].

[Graphics:../Images/NewtonCotesMod_gr_215.gif]
[Graphics:../Images/NewtonCotesMod_gr_216.gif]
[Graphics:../Images/NewtonCotesMod_gr_217.gif]

The function  [Graphics:../Images/NewtonCotesMod_gr_218.gif]  is the lowest power of  x  for which the Boole's rule is not exact.

 

[Graphics:../Images/NewtonCotesMod_gr_219.gif]


[Graphics:../Images/NewtonCotesMod_gr_220.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004