# 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.

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 DD(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.
d) Dkf(x,y)dA=kDf(x,y)dA (Scalar Multiple Property).
e) If f(x,y)g(x,y) for all (x,y)D then Df(x,y)dADg(x,y)dA.
f) ∣∣∣Df(x,y)dA∣∣∣Df(x,y)dA.
g) If D1,D2,...,DnD(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=1Dkf(x,y)dA (Additivity of Domains Property) by Double Integral.