I ended up using recordMyDesktop with the qt frontend, both of which were in the standard Mandriva repositories. You can select an area of the screen to record via the main window, but there is also a tray icon. Initiating a recording from the tray icon seems to always grab the whole screen, regardless of what is selected.
Additionally, the selection only seems to work if you choose the box and then hit record on the main window. Stopping that recording and then clicking record a second time results in having a full-desktop recording, which is not what I wanted. These complications caused me to have to throw away three reasonable takes, because it was easier to recreate them then to figure out how to crop a whole video. (Although if someone knows how to do that on Mandriva, let me know.)
With an acceptable take--although I forgot one important point, but am not willing to try yet again--I uploaded the file to YouTube. RecordMyDeskop produces Ogg Theora video output with Ogg Vorbis audio, which I think is great as a supporter of open formats. YouTube happily accepted the upload, recognizing it as Theory+Vorbis, and did its magical processing. The end result, unfortunately, had completely garbled video, just some colored flecks on the screen, while the audio worked fine.
A little scouring of the Web, and I discovered a Devede, a Linux application for mastering DVDs that can also be used to convert to AVI video format. After installing the requisite codecs, I was able to convert the ogv into avi, and I uploaded that to YouTube. Somehow it got confused and thought I cancelled the upload, so I had to do this twice, but the final one stuck.
This worked for me, but if anyone knows of a simpler and more streamlined process, I'm open to ideas.