Volume of two regions using double integration

[farmd684]

Homework Statement

The region enclosed by xy=1 and x=2 hence evaluate
<br /> \iint x e^{-x} dydx<br />

Homework Equations

The Attempt at a Solution

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

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

Is this correct ?

Thanks

 

[Mark44]

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.

 

[farmd684]

Thanks :-)