FindRoot with Integration does not give results?

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1

Hi all!
I am trying to solve a system of equations (see attached nb) using FindRoot. The equations involve integration and the limits to integration must be found by the solver along with other variables. However, FindRoot does not given any solution and returns error “some components are not equations” (when the system defined in one way) and returns " is not a list of numbers with dimensions {18} at …" when FindRoot used differently. Both are presented at the end of the notebook.
I would be very thankful if someone could help with understanding the problem.

Best,
Zee

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Part 2.nb (50.1 KB)

2

Isn’t the issue that avN = Integrate[x*f[x_]/(1 - F[x]), {x, a0N, 1}] doesn’t converge on {a0N, 1} ? (Also, you need to remove the underscore in f[x_].)

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Thanks for the response Jim! I did remove the underscore, thanks for pointing out. It is true that I have this convergence problem but usually Mathematica gives some result anyway. Now it just does not give any output at all. I also tried NSolve which does not work either.