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How to calculate Mokou's double integral?

Anonymous Sun 17 Jan 08:40:32 2021 No.12591932 View Reply Original Report

Quoted By: >>12591967 >>12591976

How to calculate double integral with trigonometric function?
$\int_{-\pi}^{\pi}\int_{-\pi}^{\pi}\frac{1-\cos(x-y)}{3-\cos(x)-\cos(y)-\cos(x+y)}\mathrm{d}x\mathrm{d}y$

Anonymous

Anonymous Sun 17 Jan 2021 09:04:41 No.12591967 Report

Quoted By:

>>12591932
First we could see if the function is symmetric to focus soley on [0,pi]
It seems like if we apply integration by parts a couple of times then we might be able to spot some kind of pattern but the three gives me bad vibes.
If I had to forcefully integrate this and give some sort of answer, I'd probably do some sort of substitution taking u=cos(x), see if I can give this shit upper and lower bounds to get an approximation.

Anonymous

Anonymous Sun 17 Jan 2021 09:09:36 No.12591974 Report

Quoted By:

Additiontheorem to seperate x and y and then substitute u = tan x/2
Solve the integral over x
Afterwards idk probably something similiar for the second integral

Anonymous

Anonymous Sun 17 Jan 2021 09:10:37 No.12591976 Report

Quoted By:

>>12591932
english lit Maj here
>polynomial approximations?

Anonymous

Anonymous Sun 17 Jan 2021 09:11:35 No.12591977 Report

Quoted By:

Develop those cosines with the addition formulas, use the relations to translate cos and sin into half-arc tangents, and you fall back to an integral of a rational function. This is freshman shit.

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