MATLAB: How to replace variables

MATLABvariables

This is my script
   syms x y z dS
  z = sqrt(100 - x.^2 - y.^2)
  zx = diff(z,x)
  zy = diff(z,y)
  dS=sqrt(1+zx.^2+zy.^2)
  fun = @(x,y)(x+y+sqrt(100-x.^2-y.^2).*dS)
And this appear when i run it …..
          >> Untitled3
    z =
    (- x^2 - y^2 + 100)^(1/2)
    zx =
    -x/(- x^2 - y^2 + 100)^(1/2)
    zy =
    -y/(- x^2 - y^2 + 100)^(1/2)
    dS =
    (1 - y^2/(x^2 + y^2 - 100) - x^2/(x^2 + y^2 - 100))^(1/2)
    fun = 
        @(x,y)(x+y+sqrt(100-x.^2-y.^2).*dS)
So here's my problem , i have aldready set dS = sqrt(…) but Matlab doesn't replace dS in my fun function . How do I solve this ? Thank you

Best Answer

syms x y
z = sqrt(100 - x.^2 - y.^2);
zx = diff(z,x);
zy = diff(z,y);
dS=sqrt(1+zx.^2+zy.^2);
fun = subs(x+y+sqrt(100-x.^2-y.^2).*dS);
f = matlabFunction(fun);
M = integral2(f,0,10,0,@(x)sqrt(100-x.^2));
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