green theoreom in matlab

MATLAB has a number of tools for theorem proving. The easiest to use is likely the MuPAD Notebook app, which provides an environment for symbolic mathematics and theorem proving.

Here is a sample code for the Green's theorem in MATLAB:

main.m
syms x y
P = y*exp(x*y);
Q = x*exp(x*y);
% Define the curve
x = linspace(0,1,100);
y = sqrt(x);

% Compute the line integral around the curve
int(P,diff(y),0,1) + int(Q,diff(x),0,1)

% Compute the area enclosed by the curve
diff(int(Q,y,0,sqrt(x)),x) - diff(int(P,x,0,1),y)
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This code calculates the line integral and the area enclosed by a curve defined as y = sqrt(x) from 0 to 1, using the functions P and Q.

Please note that MATLAB's theorem proving capability is limited to basic theorem proving and symbolic manipulation. For more advanced theorem proving, it's recommended to use dedicated software like Coq, HOL, or Isabelle.