Example 5.  Use the shifted Gauss-Legendre rules for n = 3 points to compute approximations for the integrals  
        [Graphics:Images/GaussianQuadMod_gr_257.gif] .  

Solution 5.

5 (a).  Find [Graphics:../Images/GaussianQuadMod_gr_258.gif].

[Graphics:../Images/GaussianQuadMod_gr_259.gif]


[Graphics:../Images/GaussianQuadMod_gr_260.gif]

[Graphics:../Images/GaussianQuadMod_gr_261.gif]
[Graphics:../Images/GaussianQuadMod_gr_262.gif]

5 (b).  Find [Graphics:../Images/GaussianQuadMod_gr_263.gif].

[Graphics:../Images/GaussianQuadMod_gr_264.gif]


[Graphics:../Images/GaussianQuadMod_gr_265.gif]

[Graphics:../Images/GaussianQuadMod_gr_266.gif]
[Graphics:../Images/GaussianQuadMod_gr_267.gif]

5 (c).  Find [Graphics:../Images/GaussianQuadMod_gr_268.gif].

[Graphics:../Images/GaussianQuadMod_gr_269.gif]


[Graphics:../Images/GaussianQuadMod_gr_270.gif]

[Graphics:../Images/GaussianQuadMod_gr_271.gif]
[Graphics:../Images/GaussianQuadMod_gr_272.gif]


[Graphics:../Images/GaussianQuadMod_gr_273.gif]

[Graphics:../Images/GaussianQuadMod_gr_274.gif]

[Graphics:../Images/GaussianQuadMod_gr_275.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004