Integration of a curve

hello, I have a X and y data points. ex: x=[2 3 5]; y=[3 6 3];

after plotting this simple curve, how do I integrate this curve? All the syntax i find on matlab integrates symbolically.

thanks in advance

Answer 1

[Mahdi]

You can use the trapz function to give you the area under the curve. In this case,

trapz(x,y)

[jchris14]

is this using a Riemann sums method? And thanks, it works

[Mahdi]

No problem. It's using the trapezoidal method.

[jchris14]

I tried verifying it. I plotted a simple function, y=x^2. I used int(y,1,2) and found the area under the curve to be 2.33. now when I took certain points from the same curve. in this case x=[-3 -2 0 2 3],y=[10 4 0 4 10] and used trapz(x,y), I got the value 22. Is there a way around this issue?

thanks

[Mahdi]

You integration limits aren't the same so the results are different; as expected. In the first case, you're using int(y,1,2) to integrate from the domain of x=1 to x=2. In the second case, you're integrating from x=-3 to x=4.

To get the same values, look at this example:

syms x1
y=x1.^2;
int(y,1,2) % This gives an answer of 2.33 as you said.

% For the second case using trapz
x=1:0.01:2 %Goes from 1 to 2 by a step size of 0.01
y=x.^2; % Generates the y-data
trapz(x,y) %Gives a result of 2.33 as required

Please note that there are round-off and numerical errors that you should be aware of.

Answer 2

[Sara]

You can use

trapz

[Tayyaba Bano]

Hi, I need to find the intergal of a curve.

my code involves FOR loop, should I use the trapz command inside the loop or outside the loop to calculate the integral? I tried both but none of them is working.

Moreover, my curve also showing the negative values for the same positive values, how can I avoid these?

I am attaching my curve and the code.

clear all;

close all;

%save 20m3_hr_centre u_original;

%save pos y;

%%load Variables

LS_pos = 'center';

Q = 10;

x_pos = 35; %position of vertical line velocity

%% plot velocity profiles at x_pos

figure(1)

for jj=1:1:10

Q = 10;

PIV(jj)=load(['250mm_',num2str(Q),'m3h_',LS_pos]); %load images

avg(jj) = length(PIV(jj).x); %get data length

%% extract average values

u_avg(:,:,jj) = PIV(jj).u_component{avg(jj),1}(:,:);

v_avg(:,:,jj) = PIV(jj).v_component{avg(jj),1}(:,:);

u_avg_x_pos(:,jj) = PIV(jj).u_component{avg(jj),1}(:,x_pos); % extract u-component at x_pos

x_coord = max(PIV(jj).y{avg(jj),1}(:,x_pos))-PIV(jj).y{avg(jj),1}(:,x_pos); %get and invert vertical coordinate

if jj>6

plot(x_coord,u_avg_x_pos(:,jj)*-1);

else

plot(x_coord,u_avg_x_pos(:,jj));

end

hold on;

end

trapz(x_coord,u_avg_x_pos(:,jj));

xlabel('x [m]');

ylabel(' u ');

%axis([0 0.12 0 1.2])

hold off;