# Double Integral Calculator

The Double Integral Calculator is a free tool that shows the resultant value of a definite double integral in the specified order. The online double integral calculator with steps from Protonstalk speeds up the calculation, displays result to you in few seconds and helps you in your work.

### Inputs

Following are the inputs required in the calculator.

1. Function to integrate
2. dA (specified order of integration)
3. Range of x
4. Range of y

Note: Have a look at the placeholders in the calculator to know the format of inputs

### Steps

Double Integral Calculator with steps :

1. In the input field, enter the function and the limits.
2. Now, click the “Calculate” button to obtain the value.
3. Finally, in the new window, the result of the double integral will be displayed.

### Outputs

Following is the output of the calculator

1. Definite double integral result

The output will come in a new browser window.

## What is Double Integral?

Basically, the double integral of a function say f(x, y) over the region R in the XY plane is defined by

$$\int \int R\;f(x,y)dA=\lim_{m,n\rightarrow \infty }\sum_{i=1}^{m}\sum_{j=1}^{n}\;f(x_{ij},y_{ij})\Delta A$$

Coming to the application of double integral:

1. It is used to evaluate the area of a region bounded by the curve of the function.
2. Double integrals are used to compute the volume under the surface.
3. It is used to calculate the average value of a two-variable function over a rectangular region.