iPhone 11 battery replacement cost and installation

These two Apple Support articles explain your options including self repair.

About genuine iPhone batteries - Apple Support

Be sure and enter your country and region at the top of the page to check your eligibility for self repair.

Self Service Repair - Apple Support

https://support.apple.com

We dont advise anyone other than Apple (from the link or in store) You might save 30 bucks but ruin a phone, after which Apple will no longer help you. We see a lot of ruined phones here.

Can I buy on line and have my guy install?

You cannot buy a genuine Apple battery online.

If you decide to buy a 3rd party battery and have someone install it, you should not expect that battery status reports like Maximum Capacity will be displayed.

Instead, you will see a message about an "Unknown Battery"

Kurtosis12 wrote:

There are no self-service parts for an iPhone 11.

And if there were, the tool hire costs more than the Apple battery repair

There are no self-service parts for an iPhone 11.

What country are you in ?