solving integral equation where the unknow is the upper limit

I have this function

function H = ICPH(T0,T,A,B,C,D)
syms x
f(x) = A+B*x+C*x^2+D*x^(-2);
H = int(f(x),x,T0,T);

end

this function work fine if I put all numerical values

example

y =8.314* ICPH(298.15, 2066, 43.471, 9.502e-3, 0.0, -0.645e5);
vpa(y,6)
ans
802482.0

however if I put this code

syms T real
g = 802482.0 == 8.314* ICPH(298.15, T, 43.471, 9.502e-3, 0.0, -0.645e5);
h5 = vpa(solve(g,T),6)
h5 = 0.585853

In the above code I was trying to solve for the T.

If I enter T manually i got the right answer put I use solve to find the unknow temperature the answer dont make sence.

h5 should be 2066.

what im doing wrong

Answer 1

[Paul]

Assuming T and T0 are positive, it looks like there are two values of T that will satisfy the equation. Not sure why your code is only showing one of them.

>> syms x A B C D T0 T
>> assume(T>0); assume(T0>0);
>> f(x) = A + B*x + C*x^2 + D*x^(-2);
>> H(T0,T,A,B,C,D) = int(f(x),x,T0,T);
>> y = 8.314*H(298.15,2066,43.471,9.502e-3,0,-0.645e5)
 
y =
 
14247542159329884584308006054643136629/17754354181814148147445760000000
 
>> vpa(y,6)
 
ans =
 
802482.0
 
>> g = y == 8.314*H(298.15,T,43.471,9.502e-3,0,-0.645e5);
>> solve(g,T)
 
ans =
 
                                                                                                                      2066
 3933927652016390222187165949689002925564648542001^(1/2)/353643035040244080625 - 1919850870251626733553/342345629274195625
 
>> vpa(ans)
 
ans =
 
                             2066.0
 0.58585343344352245862176866442733