solving integral equation where the unknow is the upper limit

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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

Accepted Answer

Paul
Paul on 1 Mar 2021
Edited: Paul on 1 Mar 2021
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

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