# Double Integral Calculator

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.

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