Integrating a fall through the Earth

This is the integral part of my main "How to mathematically calculate a fall through the Earth" video. https://youtu.be/s94Gojs3Ags

I slipped between x^2 - R^2 and R^2 - x^2. Sorry about that. Do work through it and make sure it all holds together.

Main channel here: http://youtube.com/standupmaths

Видео Integrating a fall through the Earth канала Matt_Parker_2