BC ONLYExample 3 __
Find the area inside both the circle r = 3 sin θ and the cardioid r = 1 + sin θ.
SOLUTION: Choosing an appropriate window, graph the curves on your
calculator. See Figure N7–7, where one half of the required area is shaded. Since
3 sin θ = 1 + sin θ when , we see that the desired area is twice the sum
of two parts: the area of the circle swept out by θ as it varies from plus the
area of the cardioid swept out by a radius vector as θ varies from .
Consequently .
Figure N7–7See also Questions 46 and 47 in the Practice Exercises.
BC ONLY