Free handy Triple Integral Calculator is here to calculate the triple integral of a function within a short span of time. Just provide the input function and bounds in the input section of the calculator and press on the calculate button to get the result immediately.
Triple Integral Calculator: If you are struggling to figure out the triple integral of a function you have come the right way. Take the help of our free Triple Integral Calculator tool to get the instant output for your expression. Along with this calculator, you can also learn the step by step procedure to solve the triple integral function easily. For your better understanding we have also provided an example question in the below sections.
Steps to Solve Triple Integral Function
Triple integral is similar to double integral. In triple integral, you need to calculate the integration for three different variables with respect to three variables. Check the following module to get an idea on how to solve the triple integral. Follow these guidelines and compute the function simply.
- Take any function have three variables to solve the triple integral
- First you need to perform the integration with respect to one variable to eliminate that variable.
- After integration substitute the bound values in the expression i,e upper limit – lower limit
- Important point is while performing integration with respect to one variable, you need to consider the other two variables as constants.
- After eliminating the first variable, you have to repeat the process in the same way to eliminate the remaining variable and get your answer in constant.
Example
Question: Solve ∫03∫23 ∫12 x2y2z2 dxdydz?
Solution:
Given that
∫03 ∫23 ∫12 x2y2z2 dxdydz
At first, perform integration with respect to x
∫03 ∫23 x3/3*3y2z2 dydz
Substitute the limit values in obtained expression
∫03 ∫23 y2z2 dydz [23-13/3]
=∫03 ∫23 y2z2 dydz [8-1/3]
=∫03 ∫23 y2z2 dydz [7/3]
Calculate integration with respect to y
=∫03 y3/3*7z2/3 dz
=∫03 7z2/3 dz [33-23/3]
=∫03 7z2/3 dz [27-8/3]
=∫03 7z2/3 dz [19/3]
=∫03 133z2/9 dz
Now, perform integration with respect to z
=133/9 * z3/3
Replacing the bound values
=133/9 * [33-03/3]
=133/9 * 27/3
=133
=133
∫03∫23 ∫12 x2y2z2 dxdydz= 133
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FAQs on Triple Integral Calculator
1. Where we can use triple integrals?
Triple integrals are the analog of double integrals for three dimensionals. They are used to find the volume of a three dimensional space and for adding up infinity quantities associated with points in a three dimensional region.
2. Is triple integral volume?
Triple integrals are used to find volume, just like double integrals are used to find mass, when volume of the region has variable density.
3. How do you find the volume of a triple integral?
The volume of an ellipsoid is expressed using the triple integral which is V=∭U dxdydz=∭U′abcρ2sinθdρdφdθ. By symmetry, you can find the volume of ellipsoid lying in the first octant (x≥0, y≥0, z≥0) and multiply the result by 8.
4. How to compute Triple Integrals?
Solving triple integrals is the same as double integrals. Here, you need to solve the integration of three variables in the given range. Solve the integration and substitute the range value in the obtained expression to get the answer.