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Polar Functions - Area

5047 Polar Area BC Bonus. Polar Functions - Area. BC CALCULUS. AP Calculus. REVIEW Polar Curves:. a gives the Diameter (or length of a Leaf). Circles. b < a with loop b = a Cardioid b > a no loop. Lima ζon. n (odd) = n petals n (even) = 2n petals. Rose.

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Polar Functions - Area

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  1. 5047 Polar Area BC Bonus Polar Functions - Area BC CALCULUS AP Calculus

  2. REVIEW Polar Curves: a gives the Diameter (or length of a Leaf) Circles b < a with loop b = a Cardioid b > a no loop Limaζon n(odd) = n petals n(even) = 2n petals Rose

  3. REVIEW Intersections: • Set the Equations equal and solve. • Check the pole independently in each curve.

  4. REVIEW Intersections: • Set the Equations equal and solve. • Check the pole independently in each curve.

  5. REVIEW Intersections: • Set the Equations equal and solve. • Check the pole independently in each curve.

  6. Lemma: Trig substitution

  7. Area of a Circular Sector REM: Calculus works with RADIANS.

  8. Area ofa Polar Region REM:

  9. Illustration: Find the area of the region bounded by the cardioid.

  10. Example: Find the area of the region bounded by the one leaf of the rose.

  11. Example: Region of Intersection Find the area of the region in the intersection between the curves.

  12. Example: Region between curves Find the area of the region inside the cardioid and outside the circle.

  13. LAST UPDATE • 03/19/12 • Assignment : p. 558 # 43 – 59 odd

  14. Area of a Circular Sector REM: Calculus works with RADIANS. -

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