adds interactive example (#59251)

packages/flutter/lib/src/material/tab_controller.dart

@@ -85,6 +85,59 @@ import 'constants.dart';
 /// }
 /// ```
 /// {@end-tool}
+///
+/// {@tool dartpad --template=stateless_widget_material}
+///
+/// This example shows how to listen to page updates in [TabBar] and [TabBarView]
+/// when using [DefaultTabController].
+///
+/// ```dart preamble
+/// final List<Tab> tabs = <Tab>[
+///   Tab(text: 'Zeroth'),
+///   Tab(text: 'First'),
+///   Tab(text: 'Second'),
+/// ];
+/// ```
+///
+/// ```dart
+/// Widget build(BuildContext context) {
+///   return DefaultTabController(
+///     length: tabs.length,
+///     // The Builder widget is used to have a different BuildContext to access
+///     // closest DefaultTabController.
+///     child: Builder(
+///       builder: (BuildContext context) {
+///         final TabController tabController = DefaultTabController.of(context);
+///         tabController.addListener(() {
+///           if (!tabController.indexIsChanging) {
+///             // Your code goes here.
+///             // To get index of current tab use tabController.index
+///           }
+///         });
+///         return Scaffold(
+///           appBar: AppBar(
+///             bottom: TabBar(
+///               tabs: tabs,
+///             ),
+///           ),
+///           body: TabBarView(
+///             children: tabs.map((Tab tab){
+///               return Center(
+///                 child: Text(
+///                   tab.text + ' Tab',
+///                   style: Theme.of(context).textTheme.headline5,
+///                 ),
+///               );
+///             }).toList(),
+///           ),
+///         );
+///       }
+///     ),
+///   );
+/// }
+/// ```
+/// {@end-tool}
+///
 class TabController extends ChangeNotifier {
   /// Creates an object that manages the state required by [TabBar] and a
   /// [TabBarView].