Double Integral Calculator

Set up and evaluate common double integral expressions.

Use this calculator as a study checker

Enter the problem carefully, review the interpreted input, and compare each step with your own work. Calculus results can depend on notation, variables, bounds, domains, and assumptions.

Check the method before copying the answer.
Use the examples below to test nearby problems.
Read the calculus guides for worked explanations.

Solution

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Enter an expression or choose an example to calculate.

Double Integral Examples

What this calculator is for

A double integral accumulates a function over a two-dimensional region. Students often use it for volume under a surface, mass over a lamina, and average value on a rectangle or region. Use it to check your setup, compare steps with your own work, and review the meaning of the final expression before copying it into homework.

How to read a double integral

Identify the order of integration from the differentials, such as \(dx\,dy\) or \(dy\,dx\).
Integrate the inner variable first while treating the other variable as constant.
Then integrate the remaining expression over the outer bounds.

Manual example

Problem: \(\int_0^1\int_0^2 xy\,dx\,dy\).
Inner integral: \(\int_0^2 xy\,dx=y[x^2/2]_0^2=2y\).
Outer integral: \(\int_0^1 2y\,dy=1\).

Common mistakes to avoid

Mixing up which bounds belong to which variable.
Changing the order of integration without changing the region.
Treating the other variable as if it disappears during the inner integration.

When to double-check the result

Rectangular and clearly written iterated integrals work best. For irregular regions, include the bounds exactly as assigned in your course.