How to find the Area of a segment in a circle using double integration over a polar region

[@JohnsMathsBook]

This video provides more details on polar coordinates
ruclips.net/video/IlTqx3La1UU/видео.html

[@EnniodBleu]

I have a pseudo-quantum-neutrino-rivet stuck in a planck electon-hole. How do I remove it? Anybody?
With a String-field-ultrasonic-pascal-hammer, obviously.

[@JohnsMathsBook]

Thanks for your feedback. I appreciate there are many simpler ways to skin this cat, however it was a useful problem to demonstrate the specific technique.