So you are saying this calculation can probably all be done inside the Arduino
this calculation is not a problem ,but I don't know what the arduino should do more ...
No need to start a database or anything.
Not directly, but a DB with your sensordata is often no bad idea as it allows you to change the view on the data.
Maybe you want the area over the last hour or in chunks of 15 minutes ...
I would just upload the calculated area over to Pachube/Cosm once a day.
I would say just as often as you upload the other data - or do you not upload those?
If I lose power to the device then the on-the-fly calculation would be lost?
Yep, unless you add an SD card to the Arduino, to store raw measurements and area math results. Add a RTC to get the thing robust.
Have a look at this shield - http://www.ladyada.net/make/logshield/index.html
I guess I would have to write the value to EEProm and if the device turned off then load in the old value and continue on.
I would go for SD card, depends how often you write in fact.
If you should continue depends on the duration of the black out. If it is for 3 days you cannot continue
I am guessing the calculation will still be fine given that you lost the x-value (time)?
see RTC tip above