# Numerically Solve for Upperbound on numerical Integral

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dsmalenb on 12 Feb 2019
Commented: Star Strider on 12 Feb 2019
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.

Star Strider on 12 Feb 2019
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 on 12 Feb 2019
Excellent. Thank you.
Star Strider on 12 Feb 2019
As always, my pleasure.

Walter Roberson on 12 Feb 2019
syms x
vpasolve(int(fun(x), x, 0, s) == v, s)