Originally Posted by

**eigensheep** Ok, so the question I'm looking at involves the following integral;

$\displaystyle I[y] = \int_{-\infty}^{\infty} (y'^2 + x^2y^2)\, dx$

restricted to functions with

$\displaystyle \int y^2\, dx = 1$

I'm trying to show that under the (given) assumption xy^2 --> 0 as x --> +infinity

we can write

$\displaystyle I[y] = 1 + \int_{-\infty}^{\infty} (y' + xy)^2\, dx$

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.

Help?