[asp.net] Connection String Using a Domain User?

Previously for all our asp.net applications we have been using a sysadmin user within SQL Server to connect and add/update/delete/get data. Our SQL Admin wants to delete that account and create a Domain Account so we can use that account within our .net applications.

My current connection string is:

 
name="name" connectionString="Data Source=server;Initial Catalog=database;Persist Security Info=True;User ID=user;Password=password" providerName="System.Data.SqlClient"

What would the connection string be for using a domain account?

I tried :

name="name" connectionString="Data Source=server;Initial Catalog=database;Persist Security Info=True;User ID=domain\user;Password=password" providerName="System.Data.SqlClient"

and it does not work.

Is there a different way to connect to SQL Server using a domain account?

Thank for your help.