MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
Let r1=3+cos2θ and r2=3. The curves are traced once for 0≤θ≤2π.
(a) Find all intersection points of the curves in the interval [0,2π].
(b) For each successive pair of intersection angles, decide which curve is outside the other. Summarize your results in an ordered list of open intervals.
(c) Formulate a sum of definite integrals that represents the total area of the region that lies inside r1 and outside r2 on 0≤θ≤2π.
(d) Evaluate the integrals from part (c) to obtain the exact numerical value of the area.