How do I know when an iPhone was switched off? Sometimes I go to sleep and wake to find that my battery died, and the iPhone is off. Is there any way to know when the battery died? Is there any way (or App) to know when was it switched off?

I'm using iPhone 4s with iOS 7.0.3.
There is no way to easily find out when the phone powered off due to the battery dying. You can, however, get your battery life by charging it completely (till 100%), let it die, then charge to power it up and then going to Settings > General > Usage > Time since last full charge and adding up the times for Usage and Standby.