Suppose I have a function of the form $f(x) = g(y)$? Then how am I supposed to find the mean values of $x$ or $y$?
I have the knowledge to find mean values of functions of the form $y=f(x)$ using the area under the curve but not more than that.
Although I am more interested in a generalized solution, currently I am stuck with a function of the form
$$y=\frac{kx^3}{e^{mx} -1} $$
Where $k$ and $m$ are constants. And I am interested in the mean value of $x$ i. e. $<x>$. $$ x \in (0, \infty) $$ $$ y \in (0, 1.248 \times 10^{-26}] $$ So far, I've tried to somehow represent the above function in the form of $x=f(y)$, but to no success. Even after using the McLaurin series expansion, I couldn't do it. It always translates to the form : $f(x) = g(y)$?