Question

hey guys!
I have double integral over the area region
( xy/(x+y+1) ), did any one knows how to assign the integration limits for both x, and y.?

Answer 1

Hi Yasser-Eryani,

I need more info. Are you trying to find the area of the plane region \[\frac{ xy }{ 1+x+y } = k\]
where k is 1 or some other constant, or are you doing a volume integral under the graph of \[z = \frac{ xy }{ 1+x+y }\]
on some other area in the xy-plane? If it's the first case, I would say express y as a function of x\[y = \frac{ k(x+1) }{ x-k }\]
and integrate with respect to x, being careful around the asymptote x = k. If it's the second case, you'll have the (xy)/(1+x+y) expression as the integrand and you'll need to find limits for whatever xy-region you're using as the domain.

Hope this helps!

Answer 2

Actually it's \[\frac{ xy}{x+y+1 }\le k\].