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Double Integral Calculator

Compute a double integral over a rectangle by 2D Simpson.

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∫∫_D f(x,y) dx dy
e.g. x*y

📖 Tutorial | Double Integral

1. Definition
Double integral ∫∫_D f(x,y) dxdy is the volume under z=f(x,y) over D. Over a rectangle it is an iterated integral.
2. Symbols
f(x,y)integrand
Dregion
xa,xbx bounds
ya,yby bounds
3. How it works
  • 2D composite Simpson;
  • 40×40 weighted grid;
  • Separable integrals match analytic results.
4. Steps
  1. Enter f(x,y);
  2. Enter bounds;
  3. Click Calculate.
5. Example
Example: ∫₀²∫₀¹ xy dydx = (1/2)(2)=1.
6. Pitfalls
This tool supports rectangles only;
f must be bounded and integrable;
Changing order may simplify.

❓ FAQ | Double Integral

Geometric meaning?
Volume under the surface.
Non-rectangular region?
Set up an iterated integral with variable bounds.
Why numerical?
No antiderivative needed.
Why a small error?
Simpson truncation (~1e-4).
Volume?
If f≥0, yes.