Gauss Quadrature

Deatils are shown for "single integrals" only.

For the theory of "multiple integrals", click here

  • To evaluate the integral



  • Do a variable transformation



  • Then



    where  wi  are the Gauss weights and  ti  are the Gauss points.



To download a subroutine that contains Gauss weights and points click here.







ntw





2(+/-)0.577350271.0





30.0
(+/-)0.77459667		0.88888889
0.55555555		





4(+/-)0.33998104
(+/-)0.86113631		0.65214515
0.34785485		





50.0
(+/-)0.53846931
(+/-)0.90617985		0.56888889
0.47862867
0.23692689		





6(+/-)0.23861919
(+/-)0.66120939
(+/-)0.93246951		0.46791393
0.36076157
0.17132449		





70.0
(+/-)0.40584515
(+/-)0.74153119
(+/-)0.94910791		0.41795918
0.38183005
0.27970539
0.12948497		





8(+/-)0.18343464
(+/-)0.52553241
(+/-)0.79666648
(+/-)0.96028986		0.36268378
0.31370665
0.22238103
0.10122854		





90.0
(+/-)0.32425342
(+/-)0.61337143
(+/-)0.83603111
(+/-)0.96816024		0.33023936
0.31234708
0.26061070
0.18064816
0.08127439		





10(+/-)0.14887434
(+/-)0.43339539
(+/-)0.67940957
(+/-)0.86506337
(+/-)0.97390653		0.29552422
0.26926672
0.21908636
0.14945135
0.06667134