Volume of two regions using double integration

1. Jul 9, 2010

farmd684

1. The problem statement, all variables and given/known data
The region enclosed by xy=1 and x=2 hence evaluate
$$\iint x e^{-x} dydx$$

2. Relevant equations

3. The attempt at a solution

I m confused about their bounded region and i formed this integral to evaluate the volume

$$\int_{2}^{\inf} \int_{0}^{1/x} x e^{-x} dydx$$
and i got the result 0.135

Is this correct ?

Thanks

2. Jul 9, 2010

Staff: Mentor

That's the approximate value. The exact value is e-2.

The region over which integration takes place could be described more clearly, IMO. I would describe it as the region between the graph of xy = 1, the positive x-axis, and the line x = 2.

3. Jul 9, 2010

Thanks :-)