# Double Integral Calculator | Online Calculator

The defined Double integral calculator can calculate functions of two variables f (x, Y) concerning these two variables in a closed enclosure R.

Therefore, today we will extend the concept we had of defined integral of a function on a closed interval [a, b] to the double integral defined in the enclosed enclosure r = [A, b] x [C, D].

are f (x, y) a continuous function for the values of x, and which belong to R. For a fixed and we obtain the function f(x) = f (x, Y) that is also continuous and therefore integrable in [a, b], therefore:

The function obtained, g (Y), is continuous and therefore integrable in [C, d] in such a way that we can define the double integral of the function f (x, y) the rectangle r = [A, b] x [C, d] as.

### For example, solving the double integral

We enter the function, in this case (x ^ 3 + 1) * y, and the limits of integration, 0 ≤ x ≤ 1, 0 ≤ and ≤ x.

This was a very simple example of double integral calculator, it is in your hands to delve more, is very intuitive, so you are not going to have any bigger problems.

**ALSO CHECK: Online Limit Calculator**

Check out the Example How we will calculate the problem using Double Integral calculator.

### Characteristics of Double Integral Calculator

**Theorem 1:** Let z=f(x,y) be a two variable real-valued function that is integrable over D⊆D(f). Then:**a)** If D has zero area, then ∬Df(x,y)dA=0.**b)** If D has area d, then ∬Df(x,y)k=kd.**c)** ∬D(f(x,y)+g(x,y))dA=∬Df(x,y)dA+∬Dg(x,y)dA (Addition Property).**d)** ∬Dkf(x,y)dA=k∬Df(x,y)dA (Scalar Multiple Property).**e)** If f(x,y)≤g(x,y) for all (x,y)∈D then ∬Df(x,y)dA≤∬Dg(x,y)dA.**f)** ∣∣∣∬Df(x,y)dA∣∣∣≤∬D∣f(x,y)∣dA.**g)** If D1,D2,...,Dn⊆D(f) are non-overlapping subsets of D(f) that share no interior points with each other and D=⋃nk=1Dk then ∬Df(x,y)dA=∑nk=1∬Dkf(x,y)dA (Additivity of Domains Property) by Double Integral.