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;
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