Should my application utilize database credentials for user login?
Depends on who is allowed to access your application. 

Probably not a good idea to give DB access to users since they'll be able to connect to the database directly which is probably not what you want.

If its a whitelist, maintain a list of users and if applicable which roles they hold in the database.

Run your web application using a Windows account, and grant access to that identity to the database. 

Authenticate users using Windows Authentication, dont perform password management on your own.