# Numerical Integraion over real domain of real 1d valued functions using Newton-Cotes approximation. # NB1: Error of approximation in O(f'' * (b-a)^3 ) # NB2: In practice quite usable for many common functions, like affine, trigonomatric function

Ruby_Lambda_Fun_Numerical _Integration_Trapezoid.rb

# D subset |R Domain over which we integrate - sample D = [1,10]
D = (1..10).to_a

# f:|R->|R function - sample x |-> f(x) := x^2 
f = lambda {|x| x*x}

# summation of function values over our domain
summator = lambda {|function, domain| domain.inject(0){|x,y| x += function.call(y)} }

# Integrations Driver (for real valued 1d functions only) - assumption: integration steps equidistant
Integrator = lambda {|summator, function, domain, upper, a,b|  dL = domain[0,upper-1]; dU = domain[1,upper]; h=(b-a)/(upper-1).to_f; (h/2)*(summer.call(function, dL) + summator.call(function, dU) )}

# example - integral_1^10 {x*x} dx
Integrator.call(summator, f, D, D.count, D.min, D.max)