Task Killers suck for newer android phones like yours.
Biggest power draw culprits are WIFI, GPS and of course your screen being lit. If you're not using WIFI or GPS turn them off. I have a convenient widget that came with the phone that has that has buttons for WIFI, Bluetooth, GPS ,SYNC and screen brightness. Most are toggle on/off, screen brightness is dim, medium, bright. My phone will easily make it through a full day without having to recharge it once I got the new battery.
Also the macropinch Battery app
https://play.google.com/store/apps/d...ch.pearl&hl=en
Is very unobtrusive and has a nice battery % left for your top screen. You look through advanced and see is draining you and it will tell you hours and minutes since last charge, I get 26 sometimes.