Tool to calculate triple Integral. The calculation of three consecutive integral makes it possible to compute volumes for functions with three variables to integrate over a given interval.

Triple Integral - dCode

Tag(s) : Functions, Symbolic Computation

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!

A suggestion ? a feedback ? a bug ? an idea ? *Write to dCode*!

Sponsored ads

Tool to calculate triple Integral. The calculation of three consecutive integral makes it possible to compute volumes for functions with three variables to integrate over a given interval.

The triple integral calculation is equivalent to a calculation of three consecutive integrals from the innermost to the outermost.

$$ \iiint f(x,y,z) \text{ d}x\text{ d}y\text{ d}z = \int_{(x)} \left( \int_{(y)} \left( \int_{(x)} f(x,y) \text{ d}x \right) \text{ d}y \right) \text{ d}z $$

Example: Calculate the integral of $ f(x,y,z)=xyz $ over $ x \in [0,1] $, $ y \in [0,2] $ and $ z \in [0,3] $ $$ \int_{0}^{3} \int_{0}^{2} \int_{0}^{1} xyz \text{ d}x\text{ d}y\text{ d}z = \int_{0}^{3} \int_{0}^{2} \frac{y^2,z^2}{8} \text{ d}y\text{ d}z = \int_{0}^{3} \frac{z^2}{2} \text{ d}z = \frac{9}{2} $$

Enter the function to be integrated on dCode with the desired upper and lower bounds for each variable and the calculator automatically returns the result.

The cylindrical coordinates are often used to perform volume calculations via a triple integration by changing variables:

$$ \iiint f(x,y,z) \text{ d}x\text{ d}y\text{ d}z = \iiint f(r \cos(\theta), r\sin(\theta), z) r \text{ d}r\text{ d}\theta\text{ d}z $$

The spherical coordinates are often used to perform volume calculations via a triple integration by changing variables:

$$ \iiint f(x,y,z) \text{ d}x\text{ d}y\text{ d}z = \iiint f(\rho \cos(\theta) \sin(\varphi), \rho \sin(\theta)\sin(\varphi), \rho \cos(\varphi) ) \rho^2 \sin(\varphi) \text{ d}\rho \text{ d}\theta \text{ d}\varphi $$

dCode retains ownership of the source code of the script Triple Integral online. Except explicit open source licence (indicated Creative Commons / free), any algorithm, applet, snippet, software (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt, encrypt, decipher, cipher, decode, code, translate) written in any informatic langauge (PHP, Java, C#, Python, Javascript, Matlab, etc.) which dCode owns rights will not be released for free. To download the online Triple Integral script for offline use on PC, iPhone or Android, ask for price quote on contact page !

integral,triple,function,integration,integrate,calculus,volume,derivative,antiderivative,primitive

Source : https://www.dcode.fr/triple-integral

© 2019 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaches. dCode

Feedback

▲