Integration and homogeneous functions

Source abstract

We show that integrating a (positively) homogeneous function f f on a compact domain Ω ⊂ R n \Omega \subset R^n reduces to integrating a related function on the boundary ∂ Ω \partial {\Omega } . The formula simplifies when the boundary ∂ Ω \partial {\Omega } is determined by homogeneous functions. Similar results are also presented for integration of exponentials and logarithms of homogeneous functions.