Subtracting two derivatives then store in a new function

I want to calculate a double integral using polar coordinates.

xFun = @(x, y) 3.*x.*y;
dx = @(x, y) diff(xFun, x);
yFun = @(x, y) y.^2;
dy = @(x, y) diff(yFun, y);
fun = @(x, y) minus(dx, dy);
polarfun = @(theta,r) fun(r.*cos(theta),r.*sin(theta)).*r;
res = integral2(polarfun,0,pi,1,2);
disp(res);

I have a xFun and its derivative, same as yFun. Then I subtract these two and store the result function in fun. I transform fun to polarfun(using polar coordinates method). But then i cannot find the double integral of polarfun. It says:

Operator '-' is not supported for operands of type 'function_handle'.

Error in untitled>@(x,y)minus(dx,dy) (line 5)

fun = @(x, y) minus(dx, dy);

Can you please point out my mistake and show me a way to solve this problem?

Thanks alot!

[Matt J]

You have function handles, symbolic operations, and numeric operations all mixed together. You need to decide whether you want a numeric, symbolic, or functional result.

Answer 1

[Matt J]

One possibility - symbolic differntiation then numeric integration:

syms x y r theta

xFun =  3.*x*y;

dx =  diff(xFun,x);

yFun =  y.^2;

dy =  diff(yFun,y);

fun (x,y)=  dx-dy;

polarfun (theta, r)= fun(r.*cos(theta),r.*sin(theta)).*r;

pfun=matlabFunction(polarfun);

res = integral2(pfun,0,pi,1,2)

res = 4.6667

Answer 2

[Matt J]

Another possibility- symbolic differntiation then symbolic integration:

syms x y r theta

xFun =  3.*x*y;

dx =  diff(xFun,x);

yFun =  y.^2;

dy =  diff(yFun,y);

fun (x,y)=  dx-dy;

polarfun (r ,theta)= fun(r.*cos(theta),r.*sin(theta)).*r;

res = double( int( int(polarfun,theta,0,pi),r,1,2) )

res = 4.6667

Answer 3

[Matt J]

Another possibility - numeric differntiation and integration.

xFun =  @(x,y) 3.*x.*y;

dxFun =  dfunx(xFun);

yFun =  @(x,y) y.^2;

dyFun =  dfuny(yFun);

fun = @(x,y) dxFun(x,y)-dyFun(x,y);

polarfun = @(theta,r) fun(r.*cos(theta),r.*sin(theta)).*r;


res = integral2(polarfun,0,pi,1,2)

res = 4.6667

function df=dfunx(f)

 h=1e-8;
 df=@(x,y) (f(x+h,y)-f(x,y))/h;

end

function df=dfuny(f)

 h=1e-8;
 df=@(x,y) (f(x,y+h)-f(x,y))/h;

end