Ok, so the question I'm looking at involves the following integral;
restricted to functions with
I'm trying to show that under the (given) assumption xy^2 --> 0 as x --> +infinity
we can write
I've tried integration by parts, taking out the y'^2 and various other things but get the feeling I'm missing something really obvious that allows me to do the question.
Ok, so I started by taking the y'^2 out into a separate integral since it also appears in what I want to get.
Then I'm left with an integral of x^2y^2 but the difficulty I've found arises after I've chosen which part to take as u and which as dv since eg. if dv = y^2 then I can't find v. I think I must have tried just about every combination of x, x^2, y, and y^2 but always either end up with a more complicated expression or one it's impossible to find.
Are you saying that integration by parts is what I should be using?