Double integral as the word indicates gives the double integral of the given function. It is useful in finding the area in a two dimensional figure. The first integral gives the integral for limit values of x and second integral gives the integral of limit values of y respectively.

Double integral formula is given by
Double Integral FormulaWhere (a,b) are the limits for outer integral and (c,d) are limits of inner integral respectively.

The limit of y is integrated first if the order is dydx and similarly the limits of x is integrated first if the order is taken as dxdy.

Double Integral Calculator calculates the double integral of given function and gives you the answer, if you enter the function, limits for the given variable and its order provided in a given space.
Steps to solve the Double integral:
  1. Read the given problem and observe Whether the given function is double integral.
  2. Integrate as per the order the limit of y is taken as the first preference if we take dydx and similarly the limits of x is taken as the first preference if we take dxdy.
  3. After integrating each variables apply limit and then proceed for next variable. Finally simplify it and get the answer.

Below are given some problems on Double integral which may be helpful for you.

Solved Examples

Question 1: Evaluate the integral $\int_{0}^{1}$ $\int_{0}^{2}$ 3xy dx dy
Solution:
 
The double integral is
I = $\int_{0}^{1}$ $\int_{0}^{2}$ 3xy dx dy
 = $\int_{0}^{1}$ 3xy dx dy ($\int_{0}^{2}$ 3xy dy) dx
 = $\int_{0}^{1}$ [$\frac{3xy^{2}}{2}$] $|^{2}_{0}$ dx
= $\int_{0}^{1}$ 6x dx
= $\frac{6x^{2}}{2}$ $|^{1}_{0}$
= 3.

 

Question 2: Evaluate $\int_{0}^{1}$ $\int_{0}^{1}$ dx dy
Solution:
 
The double integral is I = $\int_{0}^{1}$ $\int_{0}^{1}$ dx dy
                                 = $\int_{0}^{1}$ x dy
                                 = $\int_{0}^{1}$ 1 dy
                                 = y $|^{1}_{0}$
                                 = 1.