Imagine we have a function f(x,y). For simplicity, let's say:
$$f(x, y) = \begin{cases} c & \text{if } 0 \leq x \leq 1 \text{ and } 0 \leq y \leq 1 \\ 0 & \text{otherwise} \end{cases}$$
With so much imagination, think this is the function:
I know how to integrate with respect to x, and how to integrate with respect to y. But what if I want to integrate with respect to a different direction? In example the diagonal? How do I transform the function so that I can have something as:
I would expect the result of the integral (with respect to our 'new x') to be a function:
I need it specially for distributions, but I assume the concept is the same.
Sorry for my being so naive, but I didn't even know how to ask for this in google.