Why does x vanish at infinity in momentum expectation derivation?

[A_B]

Hi,

I'm working through Griffiths' Introduction to QM, In the derivation for the expectation value of momentum, he uses that
$$\left( x \left. \left( \Psi^* \frac{\partial\Psi}{\partial x} - \frac{\partial \Psi^*}{\partial x}\Psi \right) \right) \right|_{-\infty}^{+\infty} = 0$$

Why is this so? It's easy to see that this is zero if the x weren't there, but I can't figure out why the limits are zero with the x in.

Thanks,
A_B

 

[Liquidxlax]

since you said that it's easy to see that this is zeero if the x weren't there, wouldn't that mean by your reasoning that everything inside the brackets would equal zero.

 

[A_B]

I'm sorry, the x is included in the evaluation, I edited the first post to make that clear, thanks.