why anonymous function is needed ?

i am currently confusing with this question,i try to search in matlab but all i get is the way to use the anonymous function =@ .

I try without using the anonymous function and this is what i got,

>> f= x^3 + x^2 + 3*x + 4;
>> Myareaofcurve(f,2,6,100)
Attempted to access f(2); index out of bounds because numel(f)=1.

Error in Myareaofcurve (line 18)
            sum_even = ........

with =@

>> f= @(x) x^3 + x^2 + 3*x + 4;
>> Myareaofcurve(f,2,6,100)

Area_using_simpsonsrule =

    453.3333

I need to know why.

Answer 1

[Walter Roberson]

= x^3 + x^2 + 3*x + 4; would require that x already been given a definite value, and it would calculate f as being a particular numeric value. The x would have to be a numeric scalar or a square two-dimensional array for that code to work. For example if x = 3 before that, then f would be assigned the single scalar value 49. You then pass that numeric f into the routine that tries to access the numeric array as a function, and that of course fails.

= @(x) x^3 + x^2 + 3*x + 4; would define a rule, that f is to be a function that expects a single argument that for the purposes of the call will be known as x. For any one call, the x that is passed in to the function is to have the formula applied to it and the result returned. If a different argument is provided then a different result would be calculated.

= @(x) x^3 + x^2 + 3*x + 4; is mostly equivalent to having written

function r = f(x)
  r = x^3 + x^2 + 3*x + 4;
end

but does have some subtle differences not worth discussing at the moment.

[David Young]

Now I'm curious about the differences between the two ways to define f.

[Walter Roberson]

http://blogs.mathworks.com/loren/2013/01/10/introduction-to-functional-programming-with-anonymous-functions-part-1/

[David Young]

Interesting blog post. But are there subtle differences between f defined inline and f defined in an m-file? Scope potentially, but anything else?

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/115569-what-extra-data-is-stored-by-an-anonymous-function

[David Young]

Thanks - interesting!