Multiplication of function handles and integrating it

clear all
clc
Nodes = 4;
Range_low = -pi();
Range_high = +pi();
Nodes_Size = (Range_high - Range_low)/(Nodes +1);
Nodes_Pos = [Range_low:Nodes_Size:Range_high];
j = 2;
q = @(x) (3 - sin(x)-sin(2*x)-cos(x));
f = @(x) (2*(e^(sin(x)))*(e^cos(x)));
for i = 1:(Nodes)
    
    FEL{j} = @(x) (x - Nodes_Pos(i))/Nodes_Size;
    FEL{j+1} = @(x) (Nodes_Pos(i+2) - x)/Nodes_Size;
    FER{j} = @(x) (x - Nodes_Pos(i))/Nodes_Size;
    FER{j+1} = @(x) (Nodes_Pos(i+2) - x)/Nodes_Size;
    j = j+2;
end

FEL{1} = @(x) (Nodes_Pos(2) - x)/Nodes_Size;
FEL{end +1} = @(x) (x - Nodes_Pos(end-1))/Nodes_Size;
FER{1} = @(x) (2*(e^(sin(x)))*(e^cos(x)))*(Nodes_Pos(2) - x)/Nodes_Size;
FER{end +1} = @(x) (2*(e^(sin(x)))*(e^cos(x)))*(x - Nodes_Pos(end-1))/Nodes_Size;


FE = @(x) q*FEL{1}*FEL{1};

q = integral(FE, Nodes_Pos(1),Nodes_Pos(2))

Trying to integrate a function but multiplying function handles, is giving an error I tried '.*' as well, giving the same error shown below.

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

Error in main>@(x)q*FEL{1}*FEL{1} (line 26)

FE = @(x) q*FEL{1}*FEL{1};

Error in integralCalc/iterateScalarValued (line 314)

fx = FUN(t);

Error in integralCalc/vadapt (line 132)

[q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)

[q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral (line 88)

Q = integralCalc(fun,a,b,opstruct);

Error in main (line 28)

q = integral(FE, Nodes_Pos(1),Nodes_Pos(2))

Any suggestion on how to multiply three functions and do integration

Answer 1

[Walter Roberson]

Multiplying function handles will never be supported by MATLAB. You need to invoke the handles on data and multiply the results.

FE = @(x) q*FEL{1}(x)*FEL{1}(x);

Reminder that the * operator is algebraic matrix multiplication and that integral() will always pass in a vector of x unless you use 'Arrayavalued' option. You should consider whether you really want to use * or if you want .* instead

[Ankush Kumar Mishra]

That Worked. Thanks Walter.

FE = @(x) q(x)*FEL{1}(x)*FEL{1}(x);

[Walter Roberson]

If both of them are FEL{1} then you should probably use .^2 instead of evaluating the function twice.