Integral over solid angle in Cartesian coordinates <br> bar{f} = 1/(4pi) int_{Omega} int f sin theta d theta d phi

Moselq8

Moselq8

Answered question

2022-08-12

Integral over solid angle in Cartesian coordinates
I have an integral that is an average of some (unknown) function f over solid angle: f ¯ = 1 4 π Ω f sin θ   d θ   d ϕ

Answer & Explanation

Avah Leonard

Avah Leonard

Beginner2022-08-13Added 21 answers

Step 1
The most obvious choice for the surface is a sphere of radius 1. For the sphere n ^ = r ^ , so r ^ n ^ = 1.
Step 2
Also r = 1, so 1 / r 2 = 1 on the surface. Note that you still want to use your expression for F .

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