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.
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.
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.