MATLAB: How to Double-integrate a Function with Three Variables Using quad2d

double integralintegral2quad2dsimplify

I have a question regarding double integration in MATLAB. I have three variables x, y, and z in the function I want to integrate, but want to integrate on x and y only. I am expecting the resulting equation to be a function of z, which may be more like a simplify function.

>> fun =@(x,y,z) 1/4.*max(x-(1+z)*y, 0); >> integral_fun = quad2d(fun,0,2,0,2) ??? Input argument "z" is undefined.

Error in ==> @(x,y,z)1/4.*max(x-(1+z)*y,0)

Error in ==> quad2d>tensor at 355 Z = FUN(X,Y); NFE = NFE + 1;

Error in ==> quad2d at 169 [Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Please help me out. Thank you.

Best Answer

You cannot use a numerical integration function like 'quad2d' to produce results which contain unspecified variables. That is the role played by the 'int' function of the Symbolic Toolbox. However, it should be understood that with 'int' you are not always assured of obtaining an answer; there are no known explicit answers to a great many integration problems. In the particular case you describe you would well have trouble with 'int' due to presence of the 'max' function. (My own version failed on it miserably, as I anticipated.)

Related Solutions

MATLAB: ‘I get error saying Input function must return ‘double’ or ‘single’ values. Found ‘sym’.’ because max is defined in symbolic variable, how to overcome this issue?

Your ymax function returns a sym result. If you specify the limits as function handles in your call to integral2 those function handles must return a numeric result, not a symbolic result.

If you want to integrate with a symbolic limit, work solely with symbolic variables and call the int function twice instead of calling integral2.

If you want to be able to specify b when you call integral2 rather than when you define the ymax function:

ymax = @(x, b) b.*sqrt(x);

Now when you call integral2 (I'm assuming you've defined fun, xmin, xmax, and ymin before this call) specify b:

% Use b = 1
Q = integral2(fun, xmin, xmax, ymin, @(x) ymax(x, 1));
% Use b = x.^2
Q = integral2(fun, xmin, xmax, ymin, @(x) ymax(x, x.^2));

MATLAB: Double integral with one variable

matlabFunction() by default creates a function handle that expects only as many input parameters as there are free variables in the symbolic function. You should specifically tell matlabFunction() which variables you wish to have in the calling sequence and in which order.

Best Answer

Related Solutions

MATLAB: ‘I get error saying Input function must return ‘double’ or ‘single’ values. Found ‘sym’.’ because max is defined in symbolic variable, how to overcome this issue?

MATLAB: Double integral with one variable

Related Question