Triple Integral Calculator

This evaluates a triple integral over the three regions whose antiderivatives close in elementary form: a polynomial in x, y and z over a rectangular box, an integrand c r^p z^q in cylindrical coordinates, and c rho^p in spherical coordinates, with the r and rho^2 sin(phi) from the Jacobian already included. Each answer comes with the inner integrals written out one variable at a time and a second figure worked out by Gauss-Legendre or Simpson, so an error in the algebra would show as a mismatch rather than a plausible wrong number. There is no computer algebra system behind the page, so a general integrand or a region you describe with your own surfaces is refused by name instead of guessed at. For two variables use the double integral calculator, and for one use the integral calculator.

Calculator Type

The iterated integral of a polynomial in x, y and z over a box with constant bounds, worked out exactly by the power rule in each variable.

Integrand f(x, y, z) *

A polynomial such as x^2 + y^2 + z^2 or 3xy^2z - 4. Use ^ for powers and write the letters in the order x, y, z within a term. Enter 1 for the volume of the box.

x From *

x To *

y From *

y To *

z From *

z To *

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