How can I make a integration with trapz?

Hi everyone,

I have x and y vectors, and ploted y verses x as below:

v=[2.2696;2.2696; 2.4646;2.4646;2.6775;2.6775; 2.9101;2.9101;3.1644];

x=[0 , -0.0476 , -0.0476 , -0.0952 , -0.0952 , -0.1429 , -0.1429 , -0.1905 ,-0.1905];

plot (x,v)

I want to find the inegral (The area under the curve) of curve in range of x=[0 and -0.08]. How can I do that?

Thank you in advance,

Answer 1

[Bruno Luong]

Note: The value is negative since x goes backward.

v=[2.2696;2.2696; 2.4646;2.4646;2.6775;2.6775; 2.9101;2.9101;3.1644];
x=[0  , -0.0476  , -0.0476 ,  -0.0952  , -0.0952  , -0.1429 ,  -0.1429 , -0.1905   ,-0.1905];

b=x<=0 & x>=-0.08;
xx=[x(b),-0.08];
vv=[v(b);NaN];
trapz(xx,fillmissing(vv,'previous'))

ans = -0.1879

[Davide Masiello]

I think that since the function lies all above the x axis, the area should be positive.

[Bruno Luong]

I don't compute the area but the integral with trapz with x going backward, so it return negative of the area, as noted in my answer.

Answer 2

[Davide Masiello]

I don't think you really need trapz for this function

clear,clc

x=[0,-0.0476,-0.0476,-0.0952,-0.0952,-0.1429,-0.1429,-0.1905,-0.1905];
y=[2.2696;2.2696; 2.4646;2.4646;2.6775;2.6775; 2.9101;2.9101;3.1644];

plot (x,y)

x1 = [0,-0.0476,-0.0476,-0.08];
y1 = [2.2696;2.2696; 2.4646;2.4646];

dx = diff(unique(x1,'stable'))

dx = 1×2

-0.0476 -0.0324

dy = unique(y1,'stable')'

dy = 1×2

2.2696 2.4646

area = abs(sum(dx.*dy))

area = 0.1879

[Bruno Luong]

Doesn't seem to be correct, with unique you replace the original step function by a linear function. The correct result is

2.2696*(0.0476-0)+2.4646*(0.08-0.0476)

ans = 0.1879

[Davide Masiello]

unique shouldn't be a problem since I calculate the area as sum of rectangles.

It is actually necessary in this sense.

[Bruno Luong]

Check again. There are 2 steps I give the manual formula and value above: 0.1879

[Davide Masiello]

The answer was indeed wrong because unique sorts the output unless specified otherwise. I fixed it and now it works. I also implemented to calculate the absolute value so the area comes out positive.

Thanks for pointing it out @Bruno Luong!

Answer 3

[N/A]

What should I do guys? Please inform me about the correct code

[Bruno Luong]

@shahin sharafi Only you can decide

"I want to find the inegral (The area under the curve)"

integral has sign changing with x direction, area has not.

You also stated you want using trapz.

[N/A]

Thank you for your response.