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 1199 time(s).
DoubleIntegralRK.pdf (219.12 KiB) downloaded 778 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 938 time(s).

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

GaussLegendreQuadrature.sm (60.58 KiB) downloaded 1198 time(s).
GaussLegendreQuadrature.pdf (160.77 KiB) downloaded 781 time(s).

Best regards.
Alvaro.

Wrote

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

Yes.

DoubleIntegralSteelCat.sm (47.08 KiB) downloaded 1152 time(s).
DoubleIntegralSteelCat.pdf (105.49 KiB) downloaded 618 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 956 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 956 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 1133 time(s).
DoubleIntegralJean.pdf (45.11 KiB) downloaded 690 time(s).

Best regards.
Alvaro

Wrote

Hi Jean. Yes, can copy and paste.

Thanks, Amigo !