MATLAB: Merging/Multiplying Functions

Question

Hello, I haven't figured out to find a way to create a new function out of multiplying 2 functions, for example:

fun1 = @(x) sin(x);
fun2 = @(x) cos(x);
*I want to create fun3 out of them so that -* 
fun3 = @(x) sin(x)*cos(x)

The reason I'm asking this is that if I define fun3 as-

fun3 = @(x) fun1(x)*fun2(x)

and obviously it doesn't turn into-

fun3=@(x) sin(x)*cos(x)

thus I can't integrate fun3-

integral(fun3,0,5) ~= int(sin(x)*cos(x),x,0,5)

Matlab just says-

Error using  * 
Inner matrix dimensions must agree.

Thank you

Answer 1

You need to use element-wise operations here, using the dot (.) operator for element-wise multiplication, (.*).

This works:

fun1 = @(x) sin(x);
fun2 = @(x) cos(x);
fun3 = @(x) fun1(x).*fun2(x);
int_fun3 = integral(fun3, 0, 5)
int_fun3 =
   459.7679e-003

See the documentation on Array vs. Matrix Operations for a full discussion.