# Integration of Numeric Data

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Pushkar K on 19 Jun 2023
Answered: Askic V on 20 Jun 2023
Hello, I am currently working on turbulent boundary layers and facting problem in Numeric Integration. I have a variable Beta9 ( a column vector - 3201x1 double) and rtheta59BL (a column vector - 3250x1 double). I have to integrate Beta9 over rtheta59BL. I tried to use trapez method but couldnt solve it. Could anyone please help.
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Torsten on 19 Jun 2023
Arrange the vectors such that they have the same size. Each value Beta9(i) must correspond to rtheta59BL(i).

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### Answers (1)

Askic V on 20 Jun 2023
I think this small code snippet would be sufficient to give you an idea how to proceed further:
clc;
clear;
% Just for the purpose of example
x = linspace(-4,2, 20); % 20 points
y = x.^2+2*x+5; % vector y also has 20 points
Z = trapz(x,y) % calculate area under the curve
Z = 42.0997
subplot(211)
plot(x,y);
hold on
stem(x,y);
hold off
% If there is a new vector with 50 points
x2 =linspace(-4,2,50);
% Z = trapz(x2,y); will produce an error
% First y vector needs to be interpolated with additional points
desiredNrPoints = numel(x2);
newInd = linspace(1, numel(y),desiredNrPoints);
y2 = interp1(y, newInd);
Z2 = trapz(x2,y2)
Z2 = 42.1147
subplot(212)
plot(x2,y2);
hold on
stem(x2,y2);
hold off
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