## Introduction to the Triple Integral Calculator

The triple integration calculator is an online calculator which is used to determine the triple integrand values of the respective function. It integrates the values of triple integrand through step-by-step calculations.

It is convenient and easy to use tool that gives you step-by-step instructions to solve the complicated problems of calculus. The best attribute of the triple integral solver is that it is free of cost, understandable, and gives you authentic results.

Along with this super tool, you can also use area under the graph calculator for the calculation of exact area under the curve online.

## What is the Triple Integration Calculator?

The triple integral calculator with steps means that it calculates the integrands in a three-dimensional direction. It evaluates the integrals of 3D shaped body. It calculates the volume, area, and mass of anybody whose density is variable and known.

The function which is to be calculated is expressed as:

F(x,y,z)

The order of integration on this integrand is x, y, and then z. The triple integration calculator also shows you results in the form of curves, graphs, and plots.

If function is the form of f(x,y), then using the double integrals calculator is the best option.

## How does Triple Integral Solver Work?

This 3d integral calculator finds the limit of the sum of the product of a function by following these steps:

- First of all, enter a function with respect to x, y, and z variables whose triple integrals you want to calculate.
- Choose the respective order of variables for it to differentiate e.g dxdydz, dydxdz or dzdxdy respectively.
- Select the upper and lower limits for the variables.
- Now simply hit, the “Calculate Triple Integral” button to get the results quickly.

The volume integral calculator displays the results on your screen, and the results are shown with step-wise calculations.

Right after that, if you want to know either the function is convergent or divergent then use of integral convergence calculator is quite appropriate.

## Formula Used By Triple Integral Calculator

The 3d integral calculator for solving the 3D integrals uses the following formula to get the accurate volume of three dimensional body/area. This formula is given as:

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

Here, f(x,y,z) is a 3d integrand depending upon three different variable.

Let’s learn how this triple integrals calculator uses the above mentioned formula to solve any integral

Example: A cube has sides of length 2. Let one corner be at the origin and the adjacent corners be on the positive x, y, and z axis.

If the cube’s density is proportional to the distance from the xy-plane, find its mass.

Solution: The density of the cube is f (x, y, z) = kz for some constant k.

If W is the cube, the mass is the triple integral

$$ \int \int \int W \;kz\; dV \;=\; \int_0^2 \int_0^2 \int_0^2 kz \; dx dy dz $$ $$ \int_0^2 \int_0^2 (x = 2x = 0)dy dz $$ $$ \int_0^2 \int_0^2 2kz \; dy dz $$ $$ \int_0^2 (y = 2y = 0)dy dz $$ $$ \int_0^2 4k dz \;=\; 4kdz^2 | z \;=\; 2z \;=\; 0 \;=\; 16k $$

## Attributes of Triple Integral Calculator with Steps

The triple integral solver is the integral online calculator used to solve the triple integrands of the given function with respect to different variables. It evaluates the volume and mass of the given function with respect to three different variables.

The triple integrals calculator gives you authentic results in no time. It is a free of cost tool that doesn’t charge you for any subscription payments before and after its use.

This triple integral calculator calculates the integrals in three dimensions. It also shows the results in the form of graphs, curves, and plots. It gives you reliable and easily understandable results. By using triple integration calculator, one should not worry about the accuracy and authentication of the complex problems of calculus.