Haha, I already answered that I use safari, and someone said the gfxcardstatus thing as well.
Sorry, missed that.
Im watching a video on my external screen.
Ah, if you're connecting using the TB port, the gfxCardStatus trick won't work for you, since you need the dedicated GFX (at least on the early 2011 MBPs) to do anything with the TB port.
This also explains your battery draining so fast. The 7 hour estimate is with only the integrated graphics, not running the dedicated graphics. I'd say 4 hours with an external screen running is exceptional.
And in regards to you saying that it was draining that fast before you plugged in the external screen, it's entirely possible that another program is engaging the dedicated card. All of these, and more, do:
