- #1

NotEuler

- 55

- 2

##f(y)## is nonnegative, and I know that ##\int_0^{\infty } f(y) \, dy## is finite.

I now need to calculate (or simplify) the double integral:

$$\int_0^{\infty } \left(\int_x^{\infty } f(y) \, dy\right) \, dx$$

Now, I have a conjecture that this can be written as

$$\int_0^{\infty } x f(x) \, dx$$How could I go about proving such a thing?