This video explains how to find the area of a region bounded by two circles using double integration.
In this video we are given the equation of two circles in cartesian coordinates. We learn how to convert the equations to a system of polar coordinates, convert (x,y) to the polar system (r,Θ).
The video then starts by defining the limits of integration in the r direction and provides a detailed explanation of infinitesimally small slices of Area, dA, are calculated using rdrdΘ.
Having defined the inner integral, the video then explains how to define the limits of Θ in the outer integral and demonstrate and show in detail why Θ varies between -π/2 and +π/2.
The video continues by evaluating the double integrals and finding the area bounded by the two circles.
The result is checked using the area formula πr² and subtracting the area of the inner circle from the area of the outer circle.