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 1269 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 845 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 995 time(s).

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

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1265 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 854 time(s).

Best regards.
Alvaro.

Wrote

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1219 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 677 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 1017 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 1017 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 1202 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 760 time(s).

Best regards.
Alvaro

Wrote

Hi Jean. Yes, can copy and paste.

Thanks, Amigo !