[Gretl-users] Clarification on Gauss-Legendre quadrature

Maybe this is really a clarification on the theory, not on what gretl does, but I will start by asking here. Gretl gives weights and nodes for Gauss-Legendre quadrature for arbitrary finite lower and upper limits of integration, not only the default (-1,1). Suppose I have a definite integral \int f(x) dx, with limits (a,b). I ask Gretl for help through the quadtabe command, say  for five nodes matrix GLegm = quadtable (5,2, a,b) . gretl obliges, and I get my nodes and my weights. Should I then also make the transformation  y = 2*(x-a)/(b-a)   -  1, and evaluate the integrand by [(b-a)/2]*SUM {w_i* f[a+(y_i+1)*(b-a)/2]}, where w_i are the weights I got and y_i  the nodes I got, or should I evaluate the integrand by SUM {w_i f(x_i)}, where here the nodes I got interval are represented by x_i? I ended up laughing with how confused this one has got me. The confusion stems from the question "since I adjust the nodes and weights  to the actual interval (a,b), why should I also adjust the integrand?" But I remember reading a tutorial on the matter, and it appeared to suggest that we should do both: get weights and nodes for the (a,b) interval /and /apply the transformation. Any suggestions? -- Alecos Papadopoulos PhD Athens University of Economics and Business web: alecospapadopoulos.wordpress.com/ skype:alecos.papadopoulos