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for y=18:0.001:21;

   k=[2:0.01:25];
   a1=pi*(k-2).^4/12./(1+0.8048.*(k-2)+0.1459.*(k-2).^2+1.137*10^(-3)*(k-2).^3-3.879*10^(-6)*(k-2).^4)./(exp(0.511*938.272.*k./(20*10^(y-18)*2.7*8.6170))-1);
   b1=trapz(k,a1);
da1=pi*(k-2).^4/12./(1+0.8048.*(k-2)+0.1459.*(k-2).^2+1.137*10^(-3)*(k-2).^3-3.879*10^(-6)*(k-2).^4).*(-3./(exp(0.511*938.272.*k./(20*10^(y-18)*2.7*8.6170))-1)+0.511*938.272.*k.* exp(0.511*938.272.*k./(20*10^(y-18)*2.7*8.6170))./(20*10^(y-18)*2.7*8.6170)./(exp(0.511*938.272.*k./(20*10^(y-18)*2.7*8.6170))-1).^2);
   db1=trapz(k,da1);
   
c=[25:0.1:10000]';
   a2=c.*(-86.07+50.96.*log(c)-14.45.*log(c).^2+8/3.*log(c).^3)./(1-(2.91./c+78.35./c.^2+1837./c.^3))./(exp(0.511*938.272.*c./(20*10^(y-18)*2.7*8.6170))-1);
   b2=trapz(c,a2);
da2=c.*(-86.07+50.96.*log(c)-14.45.*log(c).^2+8/3.*log(c).^3)./(1-(2.91./c+78.35./c.^2+1837./c.^3)).*(-3./(exp(0.511*938.272.*c./(20*10^(y-18)*2.7*8.6170))-1)+0.511*938.272.*c.*exp(0.511*938.272.*c./(20*10^(y-18)*2.7*8.6170))./(20*10^(y-18)*2.7*8.6170)./ (exp(0.511*938.272.*c./(20*10^(y-18)*2.7*8.6170))-1).^2);
   db2=trapz(c,da2);

dp=(db1+db2)./(b1+b2);
plot(y,dp,'r');
axis([18 21 -1 3]);
    hold on;
end

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