# Which numerical integral equation is correct?

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Szabó-Takács Beáta on 21 Jun 2019
I would have a question in connection with numerical integration in Matlab R2015b. I would like to integrate the ceilometer measured attenuated backscatter coefficient. The spatial range of backscatter coefficioent is 10 m. I should calculate the following equation:
where dz is the range (dz = 10) and β is the backscatter coefficient. The backscatter coefficient values are in range x time matrix. I tried to calculate the integral value in two different ways.
First is:
X = repmat(0,size(BS))
for j = 2:400
X(j,1)=10.*(BS(j-1,1)+BS(j,1)).*0.5+X(j-1,1);
end
X_sum = sum(X);
The second is:
TR = cumtrapz(BS);
TR_sum = sum(TR);
The resulted X and X_sum are one order of magnitude larger than TR and TR_sum. Could someone write me which calculation is correct?

R2015b

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