Amazon Instant Video customers can now AirPlay videos from their iPad or iPhone to an Apple TV. The update to the app, which lets Prime customers pick from an array of TV shows and movies free of charge, also offers improved recommendations, customer reviews, and deeper IMDB integration. Amazon says, as usual, that its app is faster and more responsive than ever before thanks to bugfixes and improvements. The new Amazon Instant Video app is available now from the App Store.