Evaluate a double integral of a polynomial in x and y over a rectangular region.
Computes the double integral ∬ f(x,y) dA over a rectangle [a,b]×[c,d] using 2D composite Simpson's rule. The method applies Simpson's 1/3 rule independently in both the x and y directions, giving O(h⁴) accuracy in each dimension.
Double integral
∬[a,b]×[c,d] f(x,y) dA ≈ (hx/3)(hy/3) Σᵢ Σⱼ wᵢ wⱼ f(xᵢ, yⱼ)
This calculator handles rectangular regions. For non-rectangular regions, you would need to express the bounds as functions of the other variable.
50 points per axis (2500 evaluations total) is usually sufficient. Increase for rapidly varying functions.