MATLAB: Area under and over the curve

area under the curve

hello I hope you can help me!

as per diagram below, I have a curve (blue) and a straight line (pink) say y=1.

I will need to find the unit area under the curve (yellow area) and "over" the curve (green area).

also the curve dont have many data points, I hope this wouldn't be a huge problem!

Please advise and many thanks in advance!

Best Answer

Try this:

xLast = find(y > 1, 1, 'last');
areaUnderCurve = sum(abs(y(1:xLast) - 1))

This is basically assuming the digitized y is a bar chart and you're summing the heights of the rectangular bars. Of use trapz() if you want trapezoids instead of rectangular bars.

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MATLAB: How to find the are between two graphs

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%1st graph %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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t=25
x1=Array_jan_13{t}.Volume;
y1=Array_jan_13{t}.Price;
%x2=Array_jan_13_s{t}.Volume_s
%y2=Array_jan_13_s{t}.Price_s
line1 = 2500*ones(1, length(x1));
%line2 = 2500*ones(1, length(x2));
x_inter=intersectPoints_jan_13{t}.x0;
y_inter=intersectPoints_jan_13{t}.y0;
 
hFig = figure
plot(x1, y1, 'r-', 'LineWidth', 2)
hold on
%plot(x2, y2, 'g-', 'LineWidth', 2)
%hold on

plot(x1, line1, 'b', 'LineWidth', 2);
hold on
%plot(x2, line2, 'b', 'LineWidth', 2);
%hold on
plot(x_inter,y_inter,'r.','markersize',18)
 
 
 
%CALCULATE THE AREA ABOVE THE DEMAND CURVE UNTIL THE INTERSECTION POINT

n=50000
%INTERPOLATE VALUES 

x1_new=linspace(x1(1),x_inter,n);
y1_new=interp1(x1,y1,x1_new);
line_fine1 = 2500*ones(1, length(x1_new));
 
 
hFig = figure
plot(x1_new, y1_new, 'r-', 'LineWidth', 2)
hold on
plot(x1_new, line_fine1, 'b', 'LineWidth', 2);
hold on
plot(x_inter,y_inter,'r.','markersize',18)
 
%Gives the position of the first element in y1_new that meets the 
%condition of being less than the condition 

indexLeft = find(y1_new < 2500, 1, 'first');
% Put up vertical where the are will be calculated

xline(x1_new(indexLeft), 'Color', 'm', 'LineWidth', 2);
%the last element in demand that intersects which will be the last element
%where the area will be calculated 

xline(x1_new(end), 'Color', 'y', 'LineWidth', 2);
% COMPUTE AREAS BETWEEN CURVE AND FLAT BLUE LINE

% Find that area below the line at 2500

%asigna los valores de x_fine desde el primer elemento hasta 
%uno antes de que la curva y fuera mayor a 1
x_area=x1_new(indexLeft : end);
y_area=line_fine1(indexLeft : end)-y1_new(indexLeft : end);
area_Loss_up = trapz(x_area, y_area)
% To double check, compute area by summing also.

area_Loss2_up = sum(y_area) * abs(x1_new(2) - x1_new(1))  % Should be fairly close.
 
 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%2ND GRAPH %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 
 
%Calculate the area between the y=2500 and supply curve 
%until the intersection point 
 
t=25
x2=Array_jan_13_s{t}.Volume_s;
y2=Array_jan_13_s{t}.Price_s;
line2 = 2500*ones(1, length(x2));
x_inter=intersectPoints_jan_13{t}.x0
y_inter=intersectPoints_jan_13{t}.y0
 
hFig = figure
plot(x2, y2, 'r-', 'LineWidth', 2)
hold on
plot(x2, line2, 'b', 'LineWidth', 2);
hold on
plot(x_inter,y_inter,'r.','markersize',18)
 
 
%CALCULATE THE AREA ABOVE THE DEMAND CURVE UNTIL THE INTERSECTION POINT
n=50000;
%INTERPOLATE VALUES 
x2_new=linspace(x_inter, x2(end),n);
y2_new=interp1(x2,y2,x2_new);
line_fine2 = 2500*ones(1, length(x2_new));
 
 
hFig = figure
plot(x2_new, y2_new, 'r-', 'LineWidth', 2)
hold on
plot(x2_new, line_fine2, 'b', 'LineWidth', 2);
hold on
plot(x_inter,y_inter,'r.','markersize',18)
 
 
 
%Gives the position of the last element in y2_new that meets the 
%condition of being less than the condition 
indexLeft = find(y2_new < 2500, 1, 'last');
% Put up vertical where the are will be calculated
xline(x2_new(indexLeft), 'Color', 'm', 'LineWidth', 2);
%the first element in demand that intersects which will be the last element
%where the area will be calculated 
xline(x2_new(1), 'Color', 'y', 'LineWidth', 2);
% COMPUTE AREAS BETWEEN CURVE AND FLAT BLUE LINE
% Find that area below the line at 2500
x_area_s=x2_new(1 : indexLeft);
y_area_s=line_fine2(1 : indexLeft)-y2_new(1 : indexLeft);
area_Loss_s_up = trapz(x_area_s, y_area_s)
% To double check, compute area by summing also.
area_Loss2_s_up= sum(y_area_s) * abs(x2_new(2) - x2_new(1)) 
 
 
 
Total_area_up=area_Loss_up+area_Loss_s_up
Total_area2_up=area_Loss2_up+area_Loss2_s_up

Best Answer

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