I have a classic probability density function in the literature of the form
$$ f(x) = \frac{4x}{\left(a^2b^2\right)} \Sigma(x, a, b) $$
where $\Sigma(x, a, b)$ is a complicated function full of arithmetic operations and $a$, $b$ are originally constants. However in my work I need to fix the value of $f(x)$ and use $a$ and $b$ as variables. More specifically, I define $b$ in terms of $a$ and solve the function as I am struggling to write this in a clear manner, this is what I did for now:
Finally, a numerical approximation allows us to solve for $a$ the equation $y = \int^{\infty}_{\text{p}} f(x, a, ac) dx$.
