If you have Windows 8 it won't work.
But it should be possible in Windows 7, you have to turn on a check for monitor something or another in Fraps settings.

In my opinion Fraps is a shitty program. It uses way too much CPU power and the file size it gives it is way too large.
I use Bandicam and it automatically detects DirectX/OpenGL games or you can select a rectangle area for it to record.

Hey dude! I have had to do this a few times and this is what i've done to get it to work

Okay so first update to the latest version of Fraps (3.5.99 i believe)
Then in the general tab of Fraps click on the "Record Aero Desktop" tickbox
Open the webpage you wish to record and get it all set up for recording
Then go to your desktop and start recording
A few seconds into the recording go to the webpage and start doing whatever you're doing.
If this doesn't work let me know and i'll do my best to help you!

I agree with madklauss - use bandicam- its free and you can easily choose the area you want to record. Try it out, you wont be dissappointed

@Madklauss The thing is all recording programs are CPU intensive and the easiest way to get around the CPU issue is to have a larger file size because it means less processing is being done during the recording.

@Epicbanana It may have changed now but bandicam has the little watermark, I guess you would call it, which if you want to look proffesional it is a little problematic.

@FestiveOnion In theory it should record the application but I think it only works in chrome from what I have noticed. If it doesn't work then it may be a good idea to look at a free alternative that you can pick the area you want to record rather than it just recording an open game.