Triple Integral Calculator

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by Alan Walker

Last Updated August 24, 2022

Introduction to Triple Integral Calculator with Steps

Triple integration calculator is an online tool which helps you evaluating multiple integrals while doing few clicks. It is very helpful for students to use online calculators for integration because they can learn these concepts quickly by doing calculations on run time.

Just like the integration by parts calculator and double integral calculator with steps, you can also evaluate definite triple integrals and indefinite triple integrals while using triple integration calculator.

Although this calculator evaluates definite and indefinite triple integrals, but both definite and indefinite integrals are different from each other.

Triple Integration Symbol

The triple integration symbol is represented as:

$$ \int\int\int $$

Find other similar calculators on this website like online washer method calculator and online disc method calculator.

Formula used by Triple Integration Calculator

Integration has different types and there are different methods along with formulas to evaluate integrals. Triple integration calculator uses below formulas to calculate step by step results:

$$ \int \int_E \int f(x,y,z) dV $$


$$ \int_{z_1}^{z_2} \left( \int_{y_1}^{y_2} \left( \int_{x_1}^{x_2} f(x,y,z)dx \right) dy \right) dz$$

Related: Learn what is partial fraction integration and how to calculate?

How Triple Integral Calculator works?

Triple integral calculator online uses the basic integration formulas but the method of evaluating the integral is different from simple integration or multiple integration.

In order to use it correctly, you got to chose either definite triple integral calculator or indefinite integral calculator along with the values of upper limit and lower limits and the variables. One you feed the values, it will uses all integration methods and formulas to calculate results.

Also find other integration tools on this platform like laplace integral calculator & fourier integral calculator to increase the efficiency and productivity regarding your integral calculations.

How to find Triple Integration Calculator with steps?

You can find this triple integral calculator step by step on our website or you can find it by doing google research. Either way, you'll reach to this online calculator which will provide you all the results you need regarding integration.

You can also find indefinite integration calculator with steps and definite integration calculator with steps on this website. All the integration calculators on this website show step by step results along with plot and graph etc.

How to use Triple Integration Calculator?

The triple integral calculator with steps is very easy to operate. You just need to follow the steps to evaluate triple integrals online:

Step 1. Enter the function you want to integrate 3 times.

Step 2. Select the type either Definite or Indefinite.

Step 3. Select the variables from the drop down in triple integral solver.

Step 4. Provide upper limit and lower limit of x variable. If you have selected the definite option.

Step 5. Provide upper limit and lower limit of y variable. If you have selected the definite option.

Step 6. Provide upper limit and lower limit of z variable. If you have selected the definite option.

Step 7. Click on "CALCULATE" button to get step by step accurate results.

Related: Use cylindrical shell method calculator to determine the surface area and volume of shells of revolution.


What does a Triple Integral Represent?

A triple integral is essentially a method of finding volume. It represents the function in three-dimensions. So, it can evaluate any function over a three-dimensional surface. It is represented as:

$$ \int \int \int f(x,y,z) dx \;dy\; dz $$

The triple integrals calculator helps to solve that type of integrals online.

How to Solve Triple Integration Problems?

The triple integrals are evaluated by integrating the function three times. The following example will help you to how to evaluate triple integral manually. But ultimatly three integral calculator is one of the best option to do it online.

$$ \int \int \int (x^2 y^2 z^2) dx \;dy\; dz \;=\; \int \int (y^2 z^2) dy \; dz $$


$$ \int \int \int (x^2 y^2 z^2) dx \;dy\; dz \;=\; \frac{x^3}{3} \int \int (y^2 z^2) dy \; dz $$

Now integration with respect to y and treating the x variable as a constant.

$$ \int \int \int (x^2 y^2 z^2) dx \;dy\; dz \;=\; \frac{x^3 y^3}{3 \times 3} \int z^2 dz $$ $$ \int \int \int (x^2 y^2 z^2) dx \;dy\; dz \;=\; \frac{x^3 y^3 z^3}{3 \times 3 \times 3} $$ $$ \int \int \int (x^2 y^2 z^2) dx \;dy\; dz \;=\; \frac{x^3 y^3 z^3}{27} $$

What are triple integral cylindrical coordinates?

These are the three-dimensional coordinates(ρ,φ,z) that used to specify a point’s location by using radial distance. These coordinates are useful in dealing with systems that has a shape like cylinder.

The triple integral graph calculator provides the step by step solution for cylindrical coordinates (ρ,φ,z).

How do you write a triple integral?

It is easy to write a triple integral using the integral sign three times and then specifying their upper and lower bounds. An indefinite triple integral is represented as,

$$ \int \int \int f(x,y,z) dx \;dy\; dz $$

So keep connect yourself with online triple integral calculator for advanced education and learning tools.

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