There is an app in the App Store called "Dpl Recorder." It is $9.99 (USD) and is in its third iteration. I've used the first version somewhat successfully; this third version does not have very good reviews.
However, it is the only app I know of that will allow you to record the screen (video) on a stock iPad.
There is a much better (and cheaper!) one for jail breakers. But, again, it's for jail broken iPads only...
Marilyn