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Find the area individually enclosed by the following Cardioids:
(A) $r = a(1 - \cos \theta)$
(B) $r = a(1 + \cos \theta)$
(C) $r = a(1 - \sin \theta)$
(D) $r = a(1 + \sin \theta)$
Player M has Php1, and Player N has Php2. Each play gives one the players Php1 from the other. Player M is enough better than player N that he wins 2/3 of the plays. They play until one is bankrupt. What is the chance that Player M wins?
Find the area bounded by $r = a \sin 3\theta$ and $r = a \cos 3\theta$.
Find the area bounded by $r = a \sin 2\theta$ and $r = a \cos 2\theta$.
Find the area enclosed by r = 2a cos2 θ.
Find the area enclosed by the following: