Gauss Legendre numerical intergration

[Sadeq]

Gauss Legendre numerical intergration
The attachment file contain solved example
i don't know how he subsitute and why a2=2 done disappear in the answer
please expalin in details

 

[lurflurf]

n=2
so
a2=1

 

[Sadeq]

n=2
so
a2=1

What about a1=2
doent apper
could u explain more pls

 

[lurflurf]

sure, we have from the handout and Gauss Legendre numerical integration
I=α₁α₁r₁²e^r₁
+α₁α₂r₁²e^r₂
+α₂α₁r₂²e^r₁
+α₂α₂r₂²e^r₂
now since n=2 we use
r₁=-1/sqrt(3)~-0.57735026918962576450914878050196
r₂=1/sqrt(3)~0.57735026918962576450914878050196
α₁=1~1.000000000000000000000000000000000
αsub]2[/sub]=1~1.000000000000000000000000000000000

So just substitute in the values to find I
I=(4/3)cosh(1/sqrt(3))
=(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(-0.57735026918962576450914878050196)²e^-0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(-0.57735026918962576450914878050196)²e^0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(0.57735026918962576450914878050196)²e^-0.57735026918962576450914878050196
+(1.000000000000000000000000000000000)(1.000000000000000000000000000000000)(0.57735026918962576450914878050196)²e^0.57735026918962576450914878050196
=1.5617973919398203851893261344599

notice that only the values of α and r for n=2 are used
The values of α and r for other n are not used
In the handout all the ones were implied

 

[Sadeq]

thank you brother