Solve Integral Problem: Find A Value

[Simon Bridge]

I am trying to find a method that gives me values of $A$ given values of $B$ and $C$.

You have been supplied with two - but you responded by asking me to work out the integral for you as well.

You have to be prepared to put some more of the work in yourself.
If you will not take advise, we cannot help you.

 

[Rochefort]

You have been supplied with two - but you responded by asking me to work out the integral for you as well.

I wanted you to prove that I could make $A$ the subject for when $n=1$ since I thought that you suggested that it was possible when using trig substitution and it didn't seem so. But you later specified

You should be able to solve for A if you used a Taylor expansion for the entire integrand.

Which I gave up on since I found it difficult to find my "order of approximation."

You can expand $\sqrt{1 - k^2 \sin^2 y}$ as a binomial series $$...$$
$\frac{B}{\sqrt{1 - k^2}} E(1,k) - C = 0$

I think that this method is easier if I can solve for $k$ but I am also finding it difficult to do so, yet I haven't given up on this method.

You have to be prepared to put some more of the work in yourself.
If you will not take advise, we cannot help you.

So I am taking advice. I just ask questions because, for me, it takes longer to solve a specific problem by myself than when I simply ask someone with more insight and experience with more advanced mathematics to guide me with hints on how to solve such a problem. So therefore you can help me, but you may chose not to for reasons such as: it is not your habit to do a lot of maths for people without getting paid for it, which is perfectly acceptable. Regardless, I will continue to put the work into this problem until I resolve it.