Integration of a function

2011 2 2
2 个回答
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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) )

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回答（2 个）

Oleg Komarov
Oleg Komarov 2011-2-2

0 个投票

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

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George
George 2011-2-2
Hello,
there is no problem with int(f,z,0,1).The problem is with int(f,z,0,x)

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Walter Roberson
Walter Roberson 2011-2-2

0 个投票

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.

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George
George 2011-2-2
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
Walter Roberson 2011-2-2
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
George 2011-2-3
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
George 2011-2-9
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
Walter Roberson 2011-2-9
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
George 2011-2-10
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
T 2013-2-27
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?

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George
George
2011-2-2

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