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