calculate area between curves

how to calculate area between these two curves??

[Chunru]

Can you include your data? You may also want to clarify if you need to consider the negative area (blue above red region).

Answer 1

[Manan Jain]

Hi!

You can use trapz function inside MATLAB for this task. It will perform the integration taking the intersection points and will give you the area under the curve.

Here is a snippet of code that might help

x = linspace(0, 10, 100);
y1 = sin(x);
y2 = cos(x);

%Plot the curves
plot(x, y1) 
hold on
plot(x, y2) 

% Find intersection points (assuming they are known)
idx1 = 20;
idx2 = 70;

% Calculate the area
area = trapz(x(idx1:idx2), abs(y1(idx1:idx2) - y2(idx1:idx2)));

disp(['Area between curves: ', num2str(area)]);

You can also refer to the trapz function in the MATLAB for further usage according to your code. I hope this might help you!

Thanks

[Tasneem Abed]

pmax =[71.42*42 80*42 90.3*42 94.71*42 101.64*42 104.16*42 108.315*42 109.62*42 113.85*42 116.095*42 119.88*42 122.1*42 123.76*42 126.56*42 129.39*42 129.39*42 129.39*42 129.39*42 126.56*42 123.76*42 122.1*42 116.095*42 109.62*42 90.3*42 80*42 71.428*42 ];

t =[7 8 9.10 9.20 9.30 9.40 9.50 10.00 10.10 10.30 10.45 11.00 11.15 11.45 12.15 13.20 14 14.30 15 15.30 16 16.30 17 18 19 19.85 ];

hold on

plot(t,pmax,'r')

hold off

data=[0 6 900;

6 7 2400;

7 15 3000;

15 18 1800;

18 22 3000;

22 24 1800];

power=data(:, 3)

Dt=data(:,2) - data(:,1)

Power_Generated=power.*Dt

Total_power1=sum(Power_Generated)

Total_power2=power.*Dt;

DATA=[data(:,1) data(:,2) power];

Average_load=Total_power2/sum(Dt);

peak_load=max(power);

Daily_LF=Average_load/peak_load*100;

Results=[Average_load peak_load*ones(size(Daily_LF)) Daily_LF];

L=length(data);

timeinterval=data(:,1:2) ;

t = sort(reshape(timeinterval,1,2*L));

for n = 1:L

P(2*n-1) = power(n);

P(2*n) = power(n);

end

hold on

plot(t,P,'b')

hold off

xlim([0 24])

grid on

grid minor

[Tasneem Abed]

it doesn't work

[Manan Jain]

Try this out.

pmax	=[71.42*42     80*42     90.3*42	94.71*42	101.64*42	 104.16*42	 108.315*42	109.62*42	113.85*42	116.095*42	119.88*42	 122.1*42	123.76*42	 126.56*42	   129.39*42    129.39*42    129.39*42    129.39*42    126.56*42   123.76*42   122.1*42   116.095*42   109.62*42   90.3*42  80*42 71.428*42  ];
t       =[7             8         9.10	    9.20	    9.30	     9.40	     9.50	    10.00	    10.10	    10.30	    10.45	     11.00	    11.15	     11.45	       12.15        13.20        14           14.30        15          15.30       16         16.30        17          18       19    19.85      ];
hold on
plot(t,pmax,'r')
hold off
data=[0 6 900;
      6 7 2400;
      7 15 3000;
      15 18 1800;
      18 22 3000;
      22 24 1800];
power=data(:, 3)
Dt=data(:,2) - data(:,1)
Power_Generated=power.*Dt
Total_power1=sum(Power_Generated)
Total_power2=power.*Dt;
DATA=[data(:,1) data(:,2) power];
Average_load=Total_power2/sum(Dt);
peak_load=max(power);
Daily_LF=Average_load/peak_load*100;
Results=[Average_load peak_load*ones(size(Daily_LF)) Daily_LF];
L=length(data);
timeinterval=data(:,1:2) ; 
t = sort(reshape(timeinterval,1,2*L));
for n = 1:L
  P(2*n-1) = power(n);
  P(2*n) = power(n);
end

hold on
plot(t,P,'b')
hold off
xlim([0 24])
grid on
grid minor

% Finding the area under the intersection
intersection = min(P(1:L), pmax(1:L));  % Select the minimum values between P and pmax
area_under_intersection = trapz(t(1:L), intersection);  % Calculate the area using the trapz function

disp(['Area under intersection: ', num2str(area_under_intersection)]);

In the code, I assume that the arrays P and pmax have the same number of elements as the length of data (denoted by L). By indexing P and pmax with (1:L), we ensure that the arrays have compatible sizes for the intersection calculation.

Please make sure that the arrays P and pmax have the correct sizes and try running the updated code.

[Tasneem Abed]

Thanks :)

[Tasneem Abed]

i want to ask the area calculated here is the selected section??

Answer 2

[Anamika]

To calculate the area between two curves in MATLAB, you can use the `trapz` function. Here's a step-by-step guide:

1. Define the x-values and the two curves, let's call them `y1` and `y2`. Make sure the curves have the same length and correspond to the same x-values.

2. Calculate the absolute difference between the two curves to obtain the vertical distance between them. Let's call it `diff_y`.

3. Use the `trapz` function to integrate the `diff_y` over the x-range. This will give you the area between the curves.

Here's an example code which shows this process:

% Defining the x-values

x = 0:0.1:10;

% Defining the two curves

y1 = sin(x);

y2 = cos(x);

% Calculating the difference between the two curves

diff_y = abs(y1 - y2);

% Calculate the area between the curves using trapz

area_between_curves = trapz(x, diff_y);

% Display the result

disp(area_between_curves);

In this example, it's calculating the area between the curves `y1` and `y2`, which are the sine and cosine functions, respectively. The `trapz` function integrates the absolute difference between the curves over the range of x-values.