Double Integral Calculator

This evaluates an iterated double integral in the one case it can do exactly: a polynomial integrand in x and y. Enter the integrand and either a rectangle, given as constant bounds in each variable, or an interval of x with a straight line above and below it, and it returns the value together with the inner integral as a polynomial, the antiderivative, the area of the region and the average value of the function over it; over a rectangle it also works the other order out and prints both, since Fubini says they agree. There is no computer algebra system behind the page, so trigonometric, exponential and logarithmic integrands, quotients, polar coordinates and curved boundaries are refused by name rather than approximated. For a single-variable integral there are separate pages for the definite and indefinite cases.

Calculator Type

The iterated integral of a polynomial over a <= x <= b and c <= y <= d, worked out exactly by the power rule in each variable.

A polynomial in x and y, such as 3x^2y + 2xy - 5. Use ^ for powers, and write x before y in a term.
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For a region that is not a rectangle: x runs between two numbers and y runs between two straight lines, which covers triangles, trapeziums and any strip with flat edges.

A polynomial in x and y, such as 3x^2y + 2xy - 5. Use ^ for powers, and write x before y in a term.
Leave the slope at 0 and the boundary is the horizontal line y = k.
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