I want to know when the app is closed, because I need to erase a Database when the user shutdown the app, just in the moment when the user close the app is the right moment to erase the SQLite Database, how can I detect this?
Supposing you don't finish() your main activity, clearing your database inside the onDestroy() method of that activity might be the closest of what you want to accomplish. As has been pointed in the comments, refer to http://developer.android.com/reference/android/app/Activity.html#ActivityLifecycle.