Defining the limits of an integral

I need to find the bounds of an integral in the following way:

I need to give an a number, which will be the value of the integral, and the output of the matlab/octave function will be b.

My code gives me a correct number, but it gives warning messages also, so what can be the problem?

This is my code: (I made it in Octave)

function first(a)
  
  f = @(x)(1/sqrt(2*pi)).*exp((-1/(x.^2)));
  intf = @(b) quad(f,-b,b);
  b = fzero(@(b) intf(b) - a,0)

endfunction

And this happens when a = 1

warning: division by zero
warning: called from
    first>@<anonymous> at line 3 column 25
    first>@<anonymous> at line 4 column 15
    first>@<anonymous> at line 5 column 26
    fzero at line 290 column 10
    first at line 5 column 5
warning: division by zero
warning: called from
    first>@<anonymous> at line 3 column 25
    first>@<anonymous> at line 4 column 15
    first>@<anonymous> at line 5 column 26
    fzero at line 290 column 10
    first at line 5 column 5
                .
                .
                .
warning: division by zero
warning: called from
    first>@<anonymous> at line 3 column 25
    first>@<anonymous> at line 4 column 15
    first>@<anonymous> at line 5 column 26
    fzero at line 290 column 10
    first at line 5 column 5
b =  2.6582

Can you help me?

Answer 1

[Star Strider]

You forgot to use element-wise operations in the division in ‘f’:

f = @(x)(1/sqrt(2*pi)).*exp((-1./(x.^2)));
                               ↑

When I corrected that and ran this:

a = 1;
f = @(x)(1/sqrt(2*pi)).*exp((-1./(x.^2)));
intf = @(b) quad(f,-b,b);
b = fzero(@(b) intf(b) - a,1)

it produced:

b =
   2.658202700888970

Note that I also changed the inital estimate from 0 to 1. That preven ts an infinite initial result.

[Jack Wilson]

Thank you!

It gives me the same warnings in Octave, but it turned out that it runs properly in Matlab!

[Star Strider]

As always, my pleasure!

I have no experience with Octave. When I did an Interweb search just now, apparently Octave handles element-wise operations with the same ‘dot’ operators, however it also appears to require them for addition and subtraction.