# How to find area enclosed between two curves?

3 views (last 30 days)
Prakash Chettri on 21 Feb 2022
Answered: Torsten on 22 Feb 2022
Lx = 150;
Ly = 150;
T0 =0;
T1 = pi/4;
T=3.175;
N=8;
W=N*T;
X0=Lx/2;
Y0=0;
W_nominal=W/2;
for a=1:2
r=rem(a,2);
if r==0
xp=0; xn=0; i=1;
while (xp>=0 && xp<=Lx/2)
XPaxisl(i)=xp+(i-1)*Lx/1200; xp=XPaxisl(i);
XNaxisl(i)=xn+(i-1)*(-Lx)/1200; xn=XNaxisl(i);
Th(i)=T0+2*((T1-T0)*(XPaxisl(i)))/Lx;
TH(i)= T0+2*((T0-T1)*(XNaxisl(i)))/Lx;
Wp(i)=W_nominal/cos(Th(i));
WP(i)=W_nominal/cos(TH(i));
ypl(i)=Wp(i)+(Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxisl(i))/Lx)))));
ynl(i)=WP(i)+(Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxisl(i))/Lx)))));
i=i+1;
end
plot(XPaxisl,ypl, '-g')
hold on
plot(XNaxisl,ynl, '-g')
hold on
end
%% shifting
r=rem(a,2);
if r==0
xp=0; xn=0; i=1; y=0; yn=0;
while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
XPaxiss1(i)=xp+(i-1)*Lx/1200; xp=XPaxiss1(i);
yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
i=i+1;
end
else
xp=0; xn=0; i=1; y=0; yn=0;
while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
XPaxiss1(i)=xp+(i-1)*Lx/1200; xp=XPaxiss1(i);
XNaxiss1(i)=xn+(i-1)*(-Lx)/1200; xn=XNaxiss1(i);
yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
yns1(i)= (a*W_nominal)+Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxiss1(i))/Lx))));
i=i+1;
end
plot(XPaxiss1,yps1, '-r')
hold on
plot(XNaxiss1,yns1, '-r')
xlim([-Lx/2 Lx/2])
ylim([-Ly/2 Ly/2])
end
end
I want to claculate the area between red and green curves using trapz but im not getting the exact result and it is showing error while calculating.can anyone tell how can i calculate area? I attached code for reference.

Torsten on 22 Feb 2022
Lx = 150;
Ly = 150;
T0 =0;
T1 = pi/4;
T=3.175;
N=8;
W=N*T;
X0=Lx/2;
Y0=0;
W_nominal=W/2;
for a=1:2
r=rem(a,2);
if r==0
xp=0; xn=0; i=1;
while (xp>=0 && xp<=Lx/2)
XPaxisl(i)=xp+(i-1)*Lx/1200; xp=XPaxisl(i);
XNaxisl(i)=xn+(i-1)*(-Lx)/1200; xn=XNaxisl(i);
Th(i)=T0+2*((T1-T0)*(XPaxisl(i)))/Lx;
TH(i)= T0+2*((T0-T1)*(XNaxisl(i)))/Lx;
Wp(i)=W_nominal/cos(Th(i));
WP(i)=W_nominal/cos(TH(i));
ypl(i)=Wp(i)+(Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxisl(i))/Lx)))));
ynl(i)=WP(i)+(Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxisl(i))/Lx)))));
i=i+1;
end
%figure(1)
plot(XPaxisl,ypl, '-g')
hold on
plot(XNaxisl,ynl, '-g')
hold on
x1 = XPaxisl;
y1 = ypl;
x2 = XNaxisl;
y2 = ynl;
end
%% shifting
r=rem(a,2);
if r==0
xp=0; xn=0; i=1; y=0; yn=0;
while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
XPaxiss1(i)=xp+(i-1)*Lx/1200; xp=XPaxiss1(i);
yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
i=i+1;
end
else
xp=0; xn=0; i=1; y=0; yn=0;
while (xp>=0 && xp<=Lx/2) && (y<=Ly/2)
XPaxiss1(i)=xp+(i-1)*Lx/1200; xp=XPaxiss1(i);
XNaxiss1(i)=xn+(i-1)*(-Lx)/1200; xn=XNaxiss1(i);
yps1(i) =(a*W_nominal)+Lx/(2*(T0-T1))*((-log(cos(T0)))+log(cos(T0+((2*(T1-T0)*XPaxiss1(i))/Lx))));
yns1(i)= (a*W_nominal)+Lx/(2*(T1-T0))*((-log(cos(T0)))+log(cos(T0+((2*(T0-T1)*XNaxiss1(i))/Lx))));
i=i+1;
end
plot(XPaxiss1,yps1, '-r')
hold on
plot(XNaxiss1,yns1, '-r')
xlim([-Lx/2 Lx/2])
ylim([-Ly/2 Ly/2])
x3 = XPaxiss1;
y3 = yps1;
x4 = XNaxiss1;
y4 = yns1;
end
end
x2=x2(end:-1:1);
y2=y2(end:-1:1);
x4=x4(end:-1:1);
y4=y4(end:-1:1);
X1 = horzcat(x2(1:end-1),x1)
Y1 = horzcat(y2(1:end-1),y1);
X2 = horzcat(x4(1:end-1),x3)
Y2 = horzcat(y4(1:end-1),y3);
%figure(2)
%plot(X1,Y1)
%hold on
%plot(X2,Y2)
%xlim([-Lx/2 Lx/2])
%ylim([-Ly/2 Ly/2])
Area = trapz(X1,abs(Y1-Y2))

Abolfazl Chaman Motlagh on 21 Feb 2022
i don't think the code you include in your question content related to what you want.
you have to vector, which are values of your curves at your grid points x.
here's an example for doing this task:
x = 0:0.1:20;
y1 = exp(x/2);
y2 = (x).^3;
dY = abs(y1-y2);
plot(x,y1,'Color','r','LineWidth',2);
hold on; grid on;
plot(x,y2,'Color','g','LineWidth',2);
plot(x,dY,'Color','b','LineWidth',2);
legend('y1 = exp(x/2)','y2= x^3','|y1-y2|','Location','best');
Diff = trapz(x,dY);
disp(['Area between 2 Curves :' num2str(Diff)])
Area between 2 Curves :26164.3149
Prakash Chettri on 22 Feb 2022
Thank you for the help. But i want to calculate area between curve given by "ypl(i)" and "yps1(i)" over x domain as XPaxisl(i) as noted in a code attached by me.

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