hello everyone!! I wanted to ask how can I write these double ıntegrals in Smath ??

u(x,y):U1*sin({3*π}/2*x-{3*π}/4)*sin({3*π}/2*y-{3*π}/4)

U1 is one and I already identified above.

int(int(diff(u(x,y),x)*diff(u(x,y),x),y,0,b),x,0,a)

a and b is also defined above.

I couldn't do a double integral with only two variables.

thank you

The Simpson rule in SMath doesn't handle double integrals even if the variable is the same.

You can use some CAS interface like Maxima.

If you want a numeric solution, in your case you could use Gauss quadrature, which is easy as you have a rectangular region.