Two circles are represented in polar form by the equations and
MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Two circles are represented in polar form by the equations r=6cosθ and r=3. The closed region D is the set of points that satisfy both r≤6cosθ and r≥3.
(a) Determine all values of θ in the interval 0≤θ≤π at which the two curves intersect.
(b) Write, but do not yet evaluate, a definite integral that represents the area of the portion of D lying above the x-axis.
(c) Evaluate your integral from part (b) and use the result to find the total area of D. Express the exact numerical value of the area.
(d) Briefly interpret why your answer in part (c) is reasonable by referring to the geometry of the two circles.