Hi!(adsbygoogle = window.adsbygoogle || []).push({});

I have to integrate on a triangular domain

[tex]

\int_T f(x,y,z)dxdydz

[/tex]

so I use simplex coordinates, i.e.

[tex]x=(1-\alpha-\beta)x_1+\alpha x_2+\beta x_3[/tex]

[tex]y=(1-\alpha-\beta)y_1+\alpha y_2+\beta y_3[/tex]

[tex]z=(1-\alpha-\beta)z_1+\alpha z_2+\beta z_3[/tex]

where [tex](x_i,y_i,z_i)[/tex] are the vertices of the triangle and [tex] 0\le\alpha\le1,\ 0\le\beta\le1-\alpha[/tex]

So what is the Jacobian? When I try to calculate it, the matrix is not square because I have two variables and three equations!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Integrate on a triangular domain

Loading...

Similar Threads for Integrate triangular domain |
---|

I How to derive this log related integration formula? |

I An integration Solution |

B I Feel Weird Using Integral Tables |

B Methods of integration: direct and indirect substitution |

A Getting a finite result from a non-converging integral |

**Physics Forums | Science Articles, Homework Help, Discussion**