How to solve the output of function "int", can not be "double" ?

Hi guys:

I have a question about function "int" and "double". Imagine I have a 2 line code as below

 a1 = int ( "some code here");
 a2 = double (a1); 

I have a problem at this 2nd line, it says "Unable to convert expression containing remaining symbolic function calls into double array. Argument must be expression that evaluates to number."

The output of this a1 is

 int((5000*exp(-23931/(5*(- (2969455571328467*u^8)/5444517870735015415413993718908291383296 + (6426478858171711*u^7)/664613997892457936451903530140172288 - (5723691213461993*u^6)/81129638414606681695789005144064 + (5410674489502443*u^5)/19807040628566084398385987584 - (2916731417316609*u^4)/4835703278458516698824704 + (7157656872368969*u^3)/9444732965739290427392 - (2342765945804471*u^2)/4611686018427387904 + (5565587976219517*u)/36028797018963968 + 1357300938508151/4398046511104))))/51, u, 0, 5999)

Anyone could give me some hint how to solve this problem? Thanks for your time.

[Star Strider]

It is always appropriate to plot the function first —

syms u 
% a1 = int((5000*exp(-23931/(5*(- (2969455571328467*u^8)/5444517870735015415413993718908291383296 + (6426478858171711*u^7)/664613997892457936451903530140172288 - (5723691213461993*u^6)/81129638414606681695789005144064 + (5410674489502443*u^5)/19807040628566084398385987584 - (2916731417316609*u^4)/4835703278458516698824704 + (7157656872368969*u^3)/9444732965739290427392 - (2342765945804471*u^2)/4611686018427387904 + (5565587976219517*u)/36028797018963968 + 1357300938508151/4398046511104))))/51, u, 0, 5999)
fcn = matlabFunction((5000*exp(-23931/(5*(- (2969455571328467*u^8)/5444517870735015415413993718908291383296 + (6426478858171711*u^7)/664613997892457936451903530140172288 - (5723691213461993*u^6)/81129638414606681695789005144064 + (5410674489502443*u^5)/19807040628566084398385987584 - (2916731417316609*u^4)/4835703278458516698824704 + (7157656872368969*u^3)/9444732965739290427392 - (2342765945804471*u^2)/4611686018427387904 + (5565587976219517*u)/36028797018963968 + 1357300938508151/4398046511104))))/51)

fcn = function_handle with value:
    @(u)exp(-2.3931e+4./(u.*7.723804895969795e-1-u.^2.*2.540031928066265e-3+u.^3.*3.789231997523553e-6-u.^4.*3.015829600535767e-9+u.^5.*1.365846264206443e-12-u.^6.*3.527497056138421e-16+u.^7.*4.834745339814215e-20-u.^8.*2.72701425712061e-24+1.543072515355733e+3)).*9.803921568627451e+1

figure
fplot(@(u)fcn(u)+0.1, [0 5999])
grid
set(gca, 'YScale','log')
xlabel('u')
ylabel('f(u)')

a1 = integral(fcn, 0, 5999)

Warning: Inf or NaN value encountered.

a1 = Inf

This may not have a solution.

.

[Walter Roberson]

syms u
inside = str2sym('(5000*exp(-23931/(5*(- (2969455571328467*u^8)/5444517870735015415413993718908291383296 + (6426478858171711*u^7)/664613997892457936451903530140172288 - (5723691213461993*u^6)/81129638414606681695789005144064 + (5410674489502443*u^5)/19807040628566084398385987584 - (2916731417316609*u^4)/4835703278458516698824704 + (7157656872368969*u^3)/9444732965739290427392 - (2342765945804471*u^2)/4611686018427387904 + (5565587976219517*u)/36028797018963968 + 1357300938508151/4398046511104))))/51')

inside = 

y = int(inside, u, 0, 5999)

y = 

inner_poly = 1/children(children(children(inside,1),1),1)

inner_poly = 

inner_roots = vpasolve(inner_poly)

inner_roots = 

Notice that the 4901.6 root is within the bounds of integration, which run from 0 to 5999.

[sun]

@Star Strider thanks for your hint. Yeah, I will plot it first in the future. However, i am sure there must be a way to get the solution. This outcome of a1 is a probability integration, in other words 0<=a1<=1. Actually, this a2 here even I know should be somehow very close to 1, like 0.95. Do you have any other suggestions ? thank you.

[sun]

@Walter Roberson thanks again for your time, Walter.

But I am not very follow your idea, could you explain it more ? What I know is, this outcome of a1 is a probability integration, in other words 0<=a1<=1. Actually, this a1 here even I know should be somehow very close to 1, like 0.95.

[sun]

@Walter Roberson hi Walter, I had few new discover about my question today. Remember this temperature Y value was not a constant ? I just changed it to a constant (295, just one example), and do the same thing with polyfit, polyval, then poly2sym. I still have the same issue, "Unable to convert expression containing remaining symbolic function calls into double array. Argument must be expression that evaluates to number."

However, if I just use the code below, I do will successfully generate all the result. So, I am confused, why piecewise will work, but not "polyfit, polyval, then poly2sym" ? or is there a way I could use piecewise for my non-constant temperture values ?

 x(u)= piecewise(0<=u<=100000,295); % even just x= 295 works as well.  

[sun]

@Walter Roberson dear walter, sorry about my mutiple replies here. I think the best way to express my question is, just give out the whole picture. if this is convenient for you, could you please the link below. thank you again for your time and kindness.

https://www.mathworks.com/matlabcentral/answers/1440014-how-to-evaluate-integral-for-given-input-function