Double Integral Calculator

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A calculator for double integrals is presented.

Double Integral

Double integral of the form \[ \displaystyle \int_{y_1}^{y_2} \int_{x_1}^{x_2} f(x,y) dx dy \]
are calculated using the calculator below. The limits of integration may be real numbers or letters such as \( a, b ,...\) as parameters.


Use of the Definite Integral Calculator

The default example (see calcultor below) is \[ \displaystyle \int_{1}^{3} \int_{y}^{2y} ( x^2+x e^y+\ln(x+y) )dx dy \] ;
1 - Enter and edit function $f(x,y)$ and click "Enter Function" then check what you have entered.
Note that the five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^3 - 2*x + 3*cos(3x-3) + e^(-4*x)).
More notes on editing functions are located below.
2 - Click "Calculate Integral". An exact and an approximate value of the definite integral are displayed.


\( f(x,y) \) =


\( x_1 \) =
\( x_2 \) =
\( y_1 \) =
\( y_2 \) =








Notes: In editing functions, use the following:
1 - The inverse trigonometric functions are entered as:     arcsin()     arccos()     arctan() and the inverse hyperbolic functions are entered as:     arcsinh()     arccosh()     arctanh()
2 - The five operators used are: + (plus) , - (minus), / (division) , ^ (power) and * (multiplication). (example: f(x) = x^2+x e^y+log(x+y) )
3 - The function square root function is written as (sqrt). (example: x sqrt(x^2+y)
4 - The exponential function is written as (e^x). (Example: e^(2*x+3y) )
5 - The log base e function is written as ln(x). (Example: ln(3x-y) )
Here are some examples of functions that you may copy and paste to practice:
x + y       x^2 + ln(y)       x+1/y       e^(x+y)      x^2+y^2
2*sin(2x-2)       e^(2x-3y)       x/sqrt(x^2-y)       x/sqrt(y-x^2)



More References and Links

Double Integrals Calculations
Double Integrals Over General Regions
Applications of Double Integrals