Integration of a function

I want to integrate fp(z) with z(0,x). I want an analytic expression.

I have done this:

f2z=@(z) 1./(z.^2+1); 
fpz=@(z) f2z(z)./quadl(f2z,0,1);

--> the answer must be:4/(pi*(1 + x^2)) but it doesn't work

sol=int('fpz','z',0,'x') 
y=solve('y=sol',x) 
xf=@ (y) y ;

and it gives me -->

sol = fpz*x 
Warning: Explicit solution could not be found. 
In solve at 81 
In sampling2 at 81 y = [ empty sym ] ,
(81 line is :y=solve('y=sol',x) )

Answer 1

[Oleg Komarov]

This is what I get:

syms z
f = 1./(z.^2+1);
sol = f./int(f,z,0,1)

sol =
      4/(pi*(z^2 + 1))

Oleg

[George]

Hello,

there is no problem with int(f,z,0,1).The problem is with int(f,z,0,x)

Answer 2

[Walter Roberson]

sol=int('fpz(z)','z',0,'x'); %different
y = solve(subs('y=sol'),x);  %different

A) You cannot use symbolic integration on a function handle.

B) When you create a variable at the Matlab level, then by default it is not known in a quoted string being passed to the MuPad level.

[George]

Hello,

i tried what you said but still the same problem..In order to use symbolic integration i must create a function file?

[Walter Roberson]

I probably should have said

sym x z

sol = int(fpz(z),z,0,x);

y = solve(subs('y=sol'),x);

Though on the other hand, instead of using subs, just use

sym y

yinv = solve(sol - y,x);

xf = @(y) yinv(y);

Having y as both the name assigned to and the name to be solved for is likely to cause problems later, such as the next time through the loop.

[George]

The first (with y=solve(subs('y=sol'),x)) worked (with wrong result) ,because i have problem with fpz.Instead having as an exit "4/pi*(1+x^2)" it gives me the "fpz= @(z)f2z(z)./quadl(f2z,0,1)"

[George]

Hello ,i did "sol=int(fpz(z).*z,0,x)" but still gives me the wrong result .It must give "4*tan^-1 /pi)

[Walter Roberson]

No, with your fpz, the integral of fpz(z)*z from 0 to x is

2*ln(x^2+1)/Pi

The result you say it "must" give is obviously wrong, as you are integrating to the indefinite endpoint x but your result has no x in it.

[George]

Sorry,i didn't wrote it right.The result is "4*tan^-1(x)/pi".I can't figure what it's going wrong here!

[T]

When I attempt to integrate functions with MATLAB, I get an error when I declare the variable:

syms x Undefined function 'syms' for input arguments of type 'char'.

What's wrong?