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I have the AirServer app on my Mac.

I use Airplay on my iPads to gets mirrored to my Mac. The Mac captures the screen demo using Quicktime.
 
Go to telestream.net and get Screenflow. It can capture your Mac, iPad and iPhone. And, it can do both audio and video. You can also download a fully functional version of Screenflow and try it out.
 
Record iOS screen

If your iOS device is running iOS 8 and your computer is running Yosemite, connect device, open quicktime player > File > new movie recording. From the chevron next to the record button, choose the camera source as the iOS device and the audio source as needed and you're off.
 
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