Use the Double Integral Calculator | Numerical 2D Integral Solver
Enter your values below. The calculator runs in your browser and shows an estimate immediately.
How the estimate is calculated
∫ from x₀ to x₁ ∫ from y₀ to y₁ f(x,y) dy dx; approximate result by composite Simpson quadrature
Example: For f(x,y)=x+y over 0≤x≤1 and 0≤y≤2, the exact integral is 3. The numerical result should be close to 3.
When this calculator is useful
Numerical integration can be useful when an exact antiderivative is hard to find or when you want to check a worked example. The bounds here describe a rectangle. If your problem uses a curved domain, rewrite it with suitable variable limits or use an integration method designed for that region.
How to use this calculator
Use parentheses to make the order of operations clear. Select x and y limits that describe a rectangular region. The expression parser supports common arithmetic and elementary functions, and the result is a numerical approximation rather than symbolic algebra.
What to keep in mind
This solver handles rectangular bounds and reasonably smooth expressions. It does not automatically integrate over curved or irregular regions, resolve singularities, or provide a proof of exactness. Numerical accuracy can be affected by discontinuities and rapidly changing functions.
Frequently asked questions
What does a double integral calculate?
It accumulates values of a function over a two-dimensional region, often representing volume, mass or another total quantity.
Can this calculator solve any region?
It integrates over a rectangle defined by independent x and y bounds. For a curved region, transform the bounds or use a tool designed for that domain.
Is the answer exact?
No. The calculator uses numerical quadrature. It is an approximation, so compare with an exact method when one is available.
Which functions are supported?
Basic arithmetic, powers and common functions such as sin, cos, tan, exp, ln, log, sqrt and abs are supported. Use x and y as variables.