A double integral calculator evaluates integrals of functions of two variables over a region in the plane. It’s used to find volumes under surfaces, areas, mass and average values in multivariable calculus, physics and engineering.
For a rectangular region, integrate one variable at a time, treating the other as a constant. For example, ∫₀² ∫₀³ (x + y) dy dx: first integrate with respect to y to get [xy + y²/2] from 0 to 3, which is 3x + 4.5. Then integrate from 0 to 2 with respect to x: [1.5x² + 4.5x] from 0 to 2 = 6 + 9 = 15.
For non-rectangular regions, the limits of the inner integral depend on the outer variable. Sketching the region is the most important step. Sometimes switching the order of integration makes a hard integral easy. For circular regions, polar coordinates help: replace dA with r dr dθ, and x² + y² with r².
Common mistakes: forgetting the extra r in polar coordinates, setting up limits in the wrong order, and mixing up dy dx with dx dy. By Fubini’s theorem, the order doesn’t change the answer for well-behaved functions over rectangles, which makes switching order a useful check.
Tips for getting accurate results from the Double Integral Calculator: double-check that every input uses the right units, enter numbers without commas or symbols, and run the calculation a second time with a quick estimate in your head to confirm the answer looks reasonable.
How to use the Double Integral Calculator on Minedit: enter your values in the fields, press calculate, and review the step-by-step breakdown under the result. If something looks off, change one input at a time to see how it affects the answer, which is also a great way to learn the math behind it.
Learn more on Wikipedia’s multiple integral article. Find integral, partial derivative and Jacobian calculators on Minedit.