Integration of Numeric Data

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.

[Torsten]

Arrange the vectors such that they have the same size. Each value Beta9(i) must correspond to rtheta59BL(i).

Answer 1

[Askic V]

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