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 1217 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 794 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 949 time(s).

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

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1216 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 801 time(s).

Best regards.
Alvaro.

Wrote

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1172 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 634 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 972 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 972 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 1146 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 713 time(s).

Best regards.
Alvaro

Wrote

Hi Jean. Yes, can copy and paste.

Thanks, Amigo !