If your database in noarchivelog mode, you have to startup your database in mount state to take COLD backup.
When you perform “backup database” command in RMAN, you hit an error like
"ORA-19602: cannot backup or copy active file in NOARCHIVELOG mode".
For taking a backup you can follow this procedure :
1- shutdown immediate;
2- startup mount;
3- backup database;
4- alter database open;
This type of backups are called COLD backup and as you see while you are taking backup, your database is out of service.
Have a nice day.