integration example
let f(x,y) = exp(-(x² + y²)) ∙ sin(x) for -2 ≤ x ≤ 2 and -2 ≤ y ≤ 2
find: 1. Find the volume |f(x,y)| in the specified x and y range 2. Find the volume |f(x,y)| only in the region where √(x² + y^²) > 0.5
local numluau = require("../numluau/numluau")
local grid_x,grid_y = 1000,1000
local x = numluau.linspace(-2, 2, grid_x)
local y = numluau.linspace(-2, 2, grid_y)
local xv,yv = numluau.meshgrid(x,y)
local Z = numluau.exp(-(xv^2 + yv^2)) * numluau.sin(xv)
local dx = numluau.diff(x)[1]
local dy = numluau.diff(y)[1]
local volume = numluau.sum(numluau.abs(Z:flatten())) * dx * dy
local f = Z[numluau.greater(xv^2 + yv^2,0.5 ^ 2)]
local volume_contained = numluau.sum(numluau.abs(f:flatten())) * dx * dy
print("volume of |f(x,y)|:\n" .. volume:item() .. "\n")
print("volume of |f(x,y)| inside √(x² + y^²) > 0.5:\n" .. volume_contained:item())