Numerically Solve for Upperbound on numerical Integral

Hi all,

I am trying to determine how to write the solver code for this example problem. I want to determine the quantitiy s for a given value v such that the following holds true. Although I have provided an explicit integrand here, I am looking for the general code to evaluate this properly with any specified integrand. I just used this one because I am not looking for an analytical solution to this example.

v = 1; % Just an example value
syms s
fun = @(x) x.^x;
vpasolve(integral(fun,x,0,s)==v,s)

The error I get is as follows:

Undefined function or variable 'x'.
vpasolve(integral(fun,x, 0,s)==v,s)

I am sure I am missing something silly. I would appreciate any help you can provide.

Answer 1

[Star Strider]

Try this:

v = 1; % Just an example value
fun = @(x) x.^x;
sval = fzero(@(s)integral(fun,0,s)-v, 1)

Check = integral(fun,0,sval)                            % Delete Later

produces:

sval =
          1.19490700802612

[dsmalenb]

Excellent. Thank you.

[Star Strider]

As always, my pleasure.

Answer 2

[Walter Roberson]

syms x
vpasolve(int(fun(x), x, 0, s) == v, s)