Solving for a boundary in an integral with known value?

The assignment has to do with calculating flame-temperature of a reaction. To to this i need to solve the problem

dH = nCp(T)dT

• dH is known for the reaction
• I have the lower boundary of the integral
• n is known
• Cp(T) is known, it shiftes at certain temperatures, all of which are known

I need to find the upper limit of this complex integral (Cp(T) is of order 5) How would I do this in matlab in general?

Answer 1

[Birdman]

One approach:

syms x n
eq=4==int(x^5+2*x^4+x^3-x^2-3,1,n);
sol=double(vpasolve(eq))
ind=find(sol>0);
%extract real solution below
sol=sol(ind);
solReal=sol(1)

Try to adapt this into your problem.

[Guster]

I assume the above solves for n @ integral-value=4?

And how would I handle the fact that my function is discontinious? As stated, it shiftes at certain temperatures. In a nutshell:

Cp(T) = Cp1(T) + 2*Cp2(T)
Cp1(T)&2 = something % 298K -> 1500K
Cp1(T)&2 = something else % 1500K -> 4000K

[Birdman]

Above solves for n.

You would take the integral up to discontinuous point. For instance if the point is 6, then:

eq=4==int(x^5+2*x^4+x^3-x^2-3,0,6)+int(x^5+2*x^4+x^3-x^2-3,6,n);

You need to divide the calculation.

Check this comment.

[Guster]

Thanks for your help, maybe you can also help on this? https://se.mathworks.com/matlabcentral/answers/373138-adding-functions-of-the-same-variable-to-form-a-new-function