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Area and Arc Length in Polar Coordinates

Area and Arc Length in Polar Coordinates. Section 10-5. The area of the region bounded by the curve between the radial lines And is given by: . Area in Polar Coordinates. 1) Find the area of the region in the plane enclosed by .

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Area and Arc Length in Polar Coordinates

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  1. Area and Arc Length inPolar Coordinates Section 10-5

  2. The area of the region bounded by the curve between the radial lines And is given by: Area in Polar Coordinates

  3. 1) Find the area of the region in the plane enclosed by Graph (polar) to find the two radial lines which form the region

  4. 1) cont’d

  5. 1) cont’d

  6. 2) Find the area inside the smaller loop of the limacon

  7. 2) cont’d

  8. Area Between Polar Curves The area of the region Between the radial lines Is given by

  9. 3) Find the area of the region that lies inside the circle and outside the cardioid Graph to find points of intersection Area of circle minus cardioid Between radial lines

  10. 3) cont’d

  11. 4) Find the area of the region outside the cardioid and inside the circle Graph to find points of intersection Area of circle minus cardioid Between radial lines

  12. 4) cont’d

  13. 4) cont’d

  14. Arc Length of Polar Curves The length of the curve as Is given by:

  15. 5) Find the length of the arc from for the cardioid

  16. 5) cont’d

  17. 5) cont’d

  18. 6) Find the length of the arc from for using calculator to integrate

  19. Videos on polar area and arc length http://www.youtube.com/watch?v=Kz_m8_ndCq8 Area http://www.youtube.com/watch?v=Ug0Af7iRhFs Area http://www.youtube.com/watch?v=331ni7xWh9Y Area http://www.youtube.com/watch?v=O4gmePIOrPg Area between curves http://www.youtube.com/watch?v=bS1cY2_0Azs Area between curves http://www.youtube.com/watch?v=L6NfGpr4RbU Arc length of polar curve

  20. Home Work Page 747 # 1-4, 7, 9, 11, 21,25, 26, 29, 41, 45, 46, 59, 60, 61, 63, 65

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