How do I change order of this multiple integral?

29 Views Asked by At

The textbook asks me to change the order and then integrate the following integral:

$$\int_0^{\infty}\int_0^x\frac{e^{-y} dy.dx}{y}$$

I am having trouble in changing the order of the integral. Please tell me how to do it, so far I've sketched a curve of $y=x$ and bounding $y=0$, but what after that?

Is $$\int_0^{\infty}\int_y^{\infty}\frac{e^{-y}dx.dy}{y}$$ correct change of order?