-- Example 3. Numerical antiderivative (integral) function

local function F(f, dx)

dx = dx or 1e-4

-- Trapezoidal numeric integration function that uses

-- upvalues 'f' and 'dx'.

return function(b)

local sum, a = 0, 0

for x = a, b, dx do

sum = sum + (f(x) + f(x + dx)) / 2 * dx

end

return sum

end

end

-- x2 = ∫ 2x dx

local x2 = F(function(x) return 2 * x end)

-- x2(0), x2(1), x2(2), x2(3) gives approx. 0, 1, 4, 9

--8<----------------------------------------------------------------------------

print(x2(0), x2(1), x2(2), x2(3))

--8<----------------------------------------------------------------------------