I am trying to integrate the region between two surfaces. Their intersection can be solved numerically. Here is the code:
[solx,soly] = vpasolve([x.^2.*y.^2+x.^2+y.^2+2*x.*y-5 == 0, x.^2.*y+x+y==0],[x,y]) % find the left and right boundaries;
xmax=solx(3) % it turns out that the third entry is the right boundary I was looking for, which is 2.419...;
xmin=solx(4) % the four entry is the left boundary, which is -2.419...;
f = @(x,y) 5-x.^2-y.^2-x.*y-(x.^2.*y.^2+x.*y); % the function to be integrated;
ymax=@(x) (-2*x+sqrt(4*x.^2-4*(1+x.^2).*(x.^2-5)))./(2*(1+x.^2)); % upper boundary;
ymin=@(x) (-2*x-sqrt(4*x.^2-4*(1+x.^2).*(x.^2-5)))./(2*(1+x.^2)); % lower boundary;
I = integral2(f,xmin,xmax,ymin,ymax) % double integral;
This gives me the error message "XMIN must be a floating point scalar". I thought by indexing into solx, I already make xmax and xmin floating point scalars. In fact, in the 2nd and 3rd lines, the displays are
xmax =
xmin =
So why are they still not floating point scalars? And how to make them floating point scalars?
P.S. I tried to replace xmin by -2.42 and xmax by 2.42. It worked. I just want to understand why the above would not work.
Thank you!
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