Wow. I so did not know that. Are you serious? Arwen sung that? Wow.
Eek! My fav song is the one Merry and Pip sang on the extended version on the FOTR. At the Green Dragon. I memorized that song. I love it! It is so uplifting and cheerful. Just a good song you could have a jolly good time with. A really fun song. There is just one word I don't know. Here it goes:
Heave, Ho, to the doddle(?) I go,
to heal my heart and drown my woe.
The rain may fall, the wind may blow,
but there's to be many months to go!
Sing to the sound of the pouring rain,
and the spring that flows from hill to plain,
better than rain or rippling brooke,
Pippin: There's a mug of beer inside this Took! 
Ok, I'm done. Thank you. Bye.