Terraria/modded Minecraft/Planetside2/Skyrim on i7 3770 integrated graphics?

Terraria=yes
minecraft= most likely unless your running ridiculous shader mods and 1024x1024 texture packs.
planetside 2= as long as all settings are on the lowest, and depending on the Ghz value of your cpu you might manage 20-30FPS (most people report this performance when using intel HD 4000 which comes with the i7 3770)
skyrim: will generally average out at around 33FPS on medium settings no AA, stuttering may occur, as it does pretty much no matter your specs, skyrim is cool like that

remember when it comes to gaming RAM will make little to no difference, as some games will only be aloud to use a certain amount of ram, unless you allocate more
Skyrim uses 4gb, more CAN NOT be allocated, this is due to the engine.
Minecraft uses 512Mb, no limit to how much can be allocated, Java FTW
terraria, well my laptop can play terraria, and it has 6gb and dogcrap parts, and overheats like hell on notepad, just to put that game's requirements into perspective
Planetside, Im not 100% sure but i believe it's 4gb max, modding this value to allocate more might result in being banned, for changing the games files, or it will be reset when ever you launch the launcher.

all in all the only worry may be planetside 2, as the low fps will allow your enemies to slap you around all day long at close range, being a sniper however might be ok.
the other possible problem may be skyrim, however it doesn't really need high fps, since your attacks don't have to be all that precise, unless your trying to be like rambo and you're running around with a bow. and 33 is on medium, you could turn it down if you really need to. there is also a mod which automatically lowers the resolution when in combat, to increase fps and help you survive, then resets to whatever you have it set in the options when combat is over, this can be found in the steam workshop.

note all the values above are for playing at 1080p, you could drop to a lower resolution and gain fps. I believe however PS2's resolution choices are limited, and are generally around you monitors res, for instance, i have a 1080p monitor. But in the options i can only set it around and above that, as in i can't drop it down to 720p