I have the following double integral, and I am struggling to solve it.
$$\int_{0}^{1} y dy \int_{y}^{1}\frac{dx}{x}\left[f(x)+g(x)\right]h \left(\frac{y}{x}\right)$$
Both $f(x)$ and $g(x)$ are known in their full analytic form. However, we do not have any information about the analytic form of the function $h\left(\frac{y}{x}\right)$.
Could someone give me a hint as to how I can go about solving this? Also, let me know if my question is missing any information.
Based on Ted Shifrin's comment, here is how I solved the problem. As I stated in my question, $f(x)$ and $g(x)$ are known.
$\int_{0}^{1}y \space dy \int_{y}^{1}\frac{dx}{x}\space[f(x)+g(x)] \space h(\frac{y}{x})$
Then,I changed the order of integration and got:
$\int_{0}^{1}x\space dx \int_{0}^{x}\frac{dy}{x} \frac{y}{x} [f(x)+g(x)]h(\frac{y}{x})$
At this point, I made a change of variable: $\frac{y}{x} = u \implies du = \frac{dy}{x}$ and $0 \leq u \leq 1$
$\int_{0}^{1}dx \space x \space[f(x)+g(x)] \int_{0}^{1}du\space u \space h(u)$
As it turns out, for the $f(x)$ and $g(x)$ given to me, the $x$ integral simply gives 0.