Double Integral Calculator

This double integral calculator uses the function, variable of integration, and bounds to calculate the double integral of any given function.

Double Integral

Using the double integral calculator above will give you a value, but what does this value you mean. If you recall, taking an integral of a function f(x) = y in the coordinate plane, the resulting value is the area underneath that curve. Similarly if you take the double integral of a function f(x,y) = z the resulting value will be the volume underneath the surface defined by that function.

This is the only use of an integral. A multiple integral can be used to find the following information:

  • The average of a function over a set
  • the momentum of inertia with respect to density, volume, and distance from axis
  • The gravitational potential energy with respect to a mass in a three dimensional space
  • The electromagnetism of an object in an electric field with respect to the charges and density.
  • Countless more

How to calculate a double integral

Calculating a double integral is very straight forward. You simply take the integral of a function f(x,y) = z with respect to z. This yields a function f(x) = y. Then you take another integral of the function f(x) = y with respect to y, and the result if some value x. This value is the volume under the surface defined by f(x,y) = z.