I am supposed to use a change of coordinates to solve this integral without solving it at all.

$$\int\limits_{0}^{1}\int\limits_{0}^{e^v} \ln x dx dy$$

I'm not really sure why though, it seems pretty straight forward integration by parts... The only possible difficulty is in evaluating it by plugging in 0 to the term:

xlnx

Any ideas?

Question

I am supposed to use a change of coordinates to solve this integral without solving it at all.

$$\int\limits_{0}^{1}\int\limits_{0}^{e^v} \ln x dx dy$$

I'm not really sure why though, it seems pretty straight forward integration by parts... The only possible difficulty is in evaluating it by plugging in 0 to the term:

xlnx

Any ideas?

kainui · Answer

My instructions were, "Using a change of variables, set up the integral but don't solve it".

zepdrix · Answer

What does v represent in the upper boundary of the x integral? :U

ganeshie8 · Answer

it should be y i guess

kainui · Answer

I don't think it represents anything, just a constant. It is supposed to be a v, not a y, I checked.

kainui · Answer

It might be a hint though to change from (x,y) to (u,v) but it seems... weird. I already solved it without a change of coordinates and I think I'll just leave the answer solved to show that I don't see what he's talking about since it seems easy enough as is haha. Really bizarre.

kainui · Answer

WOW Sorry, no wonder I was looking at the wrong problem haha.

ganeshie8 · Answer

ohh

zepdrix · Answer

:P