Hi. This worksheet shows how to use an ode solver for evaluating a double integral over the region between two functions.

DoubleIntegralRK.sm (42.67 KiB) downloaded 1295 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 865 time(s).

Best regards.
Alvaro.

Thanks Alvaro for your example.

Can the change of variable be put in the procedure definition?

Wrote

Can the change of variable be put in the procedure definition,?

Like this: yes, just opposite plot.

Double Switch [x, L].sm (6.33 KiB) downloaded 1018 time(s).

Hi. This is the double integral using Gauss Legendre quadrature.

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1295 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 878 time(s).

Best regards.
Alvaro.

Wrote

...
Can the change of variable be put in the procedure definition?

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1252 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 700 time(s).

Keisan has longer Legendre than 64, but couldn't copy/paste ?
From other source: 63, 64.

Integrate Legendre [ Wr 24 ].sm (28.98 KiB) downloaded 1043 time(s).

Wrote

Keisan has longer Legendre than 64, but couldn't copy/paste ?
From other source: 63, 64.

Integrate Legendre [ Wr 24 ].sm (28.98 KiB) downloaded 1043 time(s).

Hi Jean. Yes, can copy and paste. Do that first into excel, and from there to the small SMathMatrixEditor and finally paste in SMath.

In the attached Laguerre and Legendre coeffs for the Gauss method.

DoubleIntegralJean.sm (25.63 KiB) downloaded 1229 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 782 time(s).

Best regards.
Alvaro

Wrote

Hi Jean. Yes, can copy and paste.

Thanks, Amigo !