docs: add how to use with Nuxt

Author: fi3ework

docs/faq/integration.md

@@ -2,7 +2,7 @@
 
 ## with traditional backend
 
-### Hot Module Refresh does not work when integrating with backend
+### overlay does not display in development mode
 
 When integrating with a [traditional backend](https://vitejs.dev/guide/backend-integration.html#backend-integration), in development mode, you need to inject vite-plugin-checker's runtime manually.
 
@@ -13,3 +13,46 @@ When integrating with a [traditional backend](https://vitejs.dev/guide/backend-i
 <!-- add below for vite-plugin-checker -->
 <script type="module" src="http://localhost:5173/@vite-plugin-checker-runtime-entry"></script>
 ```
+
+## with Nuxt3
+
+### overlay does not display in development mode
+
+There're two ways to use vite-plugin-checker with Nuxt3 for now.
+
+#### Use vite-plugin-checker as a normal Vite plugin
+
+There are a few steps to do:
+
+1. Add `vite-plugin-checker` `typescript` `vue-tsc` `@types/node` as devDependencies to your Nuxt project.
+2. Create a Vue component with content:
+   ```vue
+   // vite-plugin-checker.vue
+   <script setup>
+   import('/@vite-plugin-checker-runtime-entry')
+   </script>
+   ```
+3. Import component above in the root component of your Nuxt project to have a global error overlay.
+
+   ```vue
+   <script setup lang="ts">
+   import Vpc from './vite-plugin-checker.vue'
+   </script>
+
+   <template>
+     <!-- your app code -->
+     <DevOnly>
+       <ClientOnly>
+         <Vpc />
+       </ClientOnly>
+     </DevOnly>
+   </template>
+   ```
+
+#### Enable vite-plugin-checker as a built-in Nuxt functionality
+
+::: warning
+The error overlay can not be displayed in this way, we'll try to fix this with Nuxt in the future.
+:::
+
+See Nuxt's official documentation's [typecheck section](https://nuxt.com/docs/api/commands/typecheck#nuxi-typecheck).