- #1
cholyoake
- 2
- 0
The question is:
Show that:
[itex]\int_0^1\int_x^1e^\frac{x}{y}dydx[/itex]=[itex]\frac{1}{2}[/itex](e-1)
I've tried reversing the order of integration then solving from there:
[itex]\int_0^1\int_y^1 e^{\frac{x}{y}}dxdy[/itex]
=[itex]\int_0^1[ye^\frac{x}{y}]_y^1dy[/itex]
=[itex]\int_0^1ye^\frac{1}{y}-ye^1dy[/itex]
But I can't integrate [itex]ye^\frac{1}{y}[/itex]
So either I've done something wrong when changing the order of integration or something else but I can't see how to go on from here.
Thanks,
Chris.
Show that:
[itex]\int_0^1\int_x^1e^\frac{x}{y}dydx[/itex]=[itex]\frac{1}{2}[/itex](e-1)
I've tried reversing the order of integration then solving from there:
[itex]\int_0^1\int_y^1 e^{\frac{x}{y}}dxdy[/itex]
=[itex]\int_0^1[ye^\frac{x}{y}]_y^1dy[/itex]
=[itex]\int_0^1ye^\frac{1}{y}-ye^1dy[/itex]
But I can't integrate [itex]ye^\frac{1}{y}[/itex]
So either I've done something wrong when changing the order of integration or something else but I can't see how to go on from here.
Thanks,
Chris.