In this video we look at how to find the area of the region where two circles intersect using double integration
The video explains how to convert the equation of each circles from cartesian coordinates (x, y) to polar coordinates (r, Θ).
The video describes how to define the region to be integrated. It describes the angles which Θ need to rotate through in order to cover the total area of intersection, in this example from Θ= -π/2 to Θ=π/2, and explains how symmetry can be used to reduce the number of integrals from 2 to 3 so that Θ rotates from Θ=0 to Θ=π/2.
Having defined the outer integrals the video looks in detail at how to define the limits of integration of the inner integrals in the r (radial distance) direction.
The final part of the video demonstrates how to evaluate the integrals.
Link to video providing more details on polar coordinates
https://youtu.be/IlTqx3La1UU