Hello, Gracy!
Find the area of the region that lies inside circle
and outside the cardioid
Sketch the graph.Code:| o o | o * o * o * | o::* o * | o::* o * | o:::* | o::::: o * | -o::::::* ----o-------*---------o:::::::::*---- o * | o::::::* | o::::: o * | o:::* o * | o::* o * | o * o * o * o o | |
The curves intersect when: .
. . Then: .
Due to the symmetry, we can integrate from to and double.
The shaded area is: .(Area of the circle) - (Area of the cardiod)
Therefore: .
Go for it!