function [res] = XINT(XU2,XL2,A1,B1,C1,D1,A2,B2,C2,D2,A3,B3,C3,D3)
% This function is used by Cubic Spline Rayleigh Ritz Method
% (Algoritm 11.6) to exactly integrate products of cubic
% polynomials.
 syms('AA','BB','CC','DD','EE','FF','GG','XHIGH','XLOW','I');
 C = zeros(1,10);
 AA = A1*A2;
 BB = A1*B2+A2*B1;
 CC = A1*C2+B1*B2+C1*A2;
 DD = A1*D2+B1*C2+C1*B2+D1*A2;
 EE = B1*D2+C1*C2+D1*B2;
 FF = C1*D2+D1*C2;
 GG = D1*D2;
 C(10) = AA*A3;
 C(9) = (AA*B3+BB*A3)/2;
 C(8) = (AA*C3+BB*B3+CC*A3)/3;
 C(7) = (AA*D3+BB*C3+CC*B3+DD*A3)/4;
 C(6) = (BB*D3+CC*C3+DD*B3+EE*A3)/5;
 C(5) = (CC*D3+DD*C3+EE*B3+FF*A3)/6;
 C(4) = (DD*D3+EE*C3+FF*B3+GG*A3)/7;
 C(3) = (EE*D3+FF*C3+GG*B3)/8;
 C(2) = (FF*D3+GG*C3)/9;
 C(1) = (GG*D3)/10;
 XHIGH = 0;
 XLOW = 0;
 for I = 1 : 10
 XHIGH = (XHIGH+C(I))*XU2;
 XLOW = (XLOW+C(I))*XL2;
 end;
 res = XHIGH-XLOW;