Change of variables for double integral with F(y/x)

[eljose]

i would need help with this integral:

$$\int_a^{\infty}\int_a^{\infty}dxdyF(y/x)$$

now i make the change of variable y/x=u x=v then what would be the new integration limits?..thanks.

where a can be 0 or 1

 

[dextercioby]

U can't make that substitution. I hope you see why. Depending on the shape of the function "F", you may integrate directly. The integral may very easily diverge, but that wouldn't be a catastrophe, would it...?

Daniel.

 

[mathman]

You can make u the inner integral. The limits will be a/x to inf. and you will have 1/x in the integrand. v=x is irrelevant - it doesn't change anything.