# #int int_R e^(-(xy)/2)dA# where #R#:the region bounded by #y=1/4x,y=2x,y=1/x,y=4/x# Evaluate integrals?

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#int int_R e^(-(xy)/2)dA# where #R# :the region bounded by #y=1/4x,y=2x,y=1/x,y=4/x#

##### 1 Answer

#### Explanation:

graph{(y-2x)(y-1/4 x)(y-1/x)(y-4/x)=0 [-0.5, 5, -0.5, 3]}

You will see from the drawing that you cannot just write down the limits and integrate here, so I have used the first sub that came to mind:

#{(u = xy),(v = y/x):} qquad {(x = sqrt(u/v)),(y = sqrt(uv)):}#

Jacobian:

I made this up on the hoof so make sure you're happy with it.