Evaluating this particular integral

[thelibertine1]

I'm trying to numerically evaluate an integral in a paper of the form;

∫ ƒ(Ψ) dΨ ∫ ƒ(X,Ψ) dX

The second part of the integral contains a function of both X and Ψ, yet it only needs to be integrated with respect to X. This has confused me on what to use as a value for Ψ.

I've attached the integral below (excuse the scribbling). As you can see, the last integral is evaluated for dX, but contains Ψ and X.

Any help much appreciated.

 

[AMenendez]

Have you thought about treating $\psi$ as a constant in the second integral? It doesn't appear to me that the second integral has a function of both $\chi$ and $\psi$.
Just a thought.

 

[thelibertine1]

Have you thought about treating $\psi$ as a constant in the second integral? It doesn't appear to me that the second integral has a function of both $\chi$ and $\psi$.
Just a thought.

I did think about that but in the context $\psi$ and $\chi$ are analogous to y and x coordinate system so it's like a integral over 2D space. If I chose $\psi$ as a constant... I wouldn't know what to set it as. Also, $\alpha$ is a function of $\psi$ making the second integral a function of both $\psi$ and $\chi$.

 

[AMenendez]

I see what you mean. Honestly, the way I would do it is evaluate it with respect to $\chi$ but treat $\psi$ as a constant. You don't really need to worry about "what to set $\psi$ as". When you integrate a function of $\psi$ with respect to $\chi$, you'll still get a function of $\chi$ as a result, so setting $\psi$ equal to something for the sake of doing the integral isn't much of a concern.