Our free handy Double Integral Calculator tool is aimed at giving the double integral of a function within fraction of seconds. The only one thing you need to do is just give your function and range for two variables as input and obtain the value as output immediately after hitting the calculate button.
Double Integral Calculator: Finding the definite integral for a function is similar as double integral. But in case of double integral, you need to perform the same operation twice. It is a bit difficult for anyone to get the double integral of an expression. So, we advise you to use this online Double Integral Calculator to generate your answer instany. Checkout the further sections of this article to know the detailed process with an example.
How to Compute Double Integral of a function?
People can go through the below sections to get the complete procedure to find the double integral. Follow these steps to get the answer for your function.
- Let us take any function with x and y values
- To compute the double integral of that function f(x), first perform the integration for with respect to y
- After that, substitute the x range values (a,b) in function to obtain f(b) and f(a)
- Calculate f(b)-f(a)
- Again perform integration with respect to other variable
- Repeat Step 3 and Step 4 to get the result
Example
Question: Compute ∫01(∫02xy^2dx).dy?
Answer:
Given function
f(x)=xy^2
∫xy^2=x^2y^2/2
f(0)=(0)^2y^2/2=0
f(2)=(2)^2y^2/2=2y^2
∫02xy^2dx=f(2)-f(0)
=2y^2
∫01(∫02xy^2dx).dy=∫012y^2dy
∫2y^2dy=2y^3/3
f(0)=2(0)^3/3
f(1)=2(1)^3/3=⅔
∫01(∫02xy^2dx).dy=f(1)-f(0)
=⅔-0
=2/3
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Frequently Asked Questions on Double Integral Calculator
1. What is the application of double integral?
Double integrals are mainly used to calculate the area of a region in the graph, the volume of surface, and the average value of a function of two variables over a rectangular region.
2. Does order matter in double integral?
In some cases, the order of integral is not a matter. You can change the order of integration. But you need to rewrite the iterated integral.
3. How do you solve the double integral of a function?
To calculate double integral of any function, you need to compute integral with respect to y, this removes x variable. Then, calculate integral with respect to y.
4. Can you split double integral?
According to Fubini’s theorem, we can split up double integrals into iterated integrals.
5. What is the integral used for?
Generally, integrals are used for calculating the area of a two dimensional region, and volume of a 3 dimensional object that is having curved boundary.