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10.4 Area and Length in   Polar Coordinates Area of a region bounded by the polar curve                    = (   ) and by ...
OFormula:           =       (   )or               =
Ex: Find the area enclosed by one loop ofthe four-leaved rose   =       .
Ex: Find the area enclosed by one loop ofthe four-leaved rose   =       .     :
Ex: Find the area enclosed by one loop ofthe four-leaved rose   =       .     :          /     =           /
Ex: Find the area enclosed by one loop ofthe four-leaved rose   =       .     :          /     =           /          /   ...
Ex: Find the area enclosed by one loop ofthe four-leaved rose   =       .     :          /     =           /          /   ...
Ex: Find the are of the region that lies insidethe circle  =          and outside thecardioid    = +         .
Ex: Find the are of the region that lies insidethe circle  =          and outside thecardioid    = +         .      :
Ex: Find the are of the region that lies insidethe circle  =          and outside thecardioid    = +         .        :   ...
Ex: Find the are of the region that lies insidethe circle  =          and outside thecardioid    = +         .        :   ...
Arc length of a polar curve   = (   )between     = ,       =is given by          =        +      O
Ex: Find the length of the cardioid   =   +
Ex: Find the length of the cardioid   =   +=          +
Ex: Find the length of the cardioid   =   +=          +=       ( +        ) +
Ex: Find the length of the cardioid   =   +=          +=       ( +        ) +=
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Calculus II - 18

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Stewart Calculus Section 10.4

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Calculus II - 18

  1. 1. 10.4 Area and Length in Polar Coordinates Area of a region bounded by the polar curve = ( ) and by the rays: = , = O
  2. 2. OFormula: = ( )or =
  3. 3. Ex: Find the area enclosed by one loop ofthe four-leaved rose = .
  4. 4. Ex: Find the area enclosed by one loop ofthe four-leaved rose = . :
  5. 5. Ex: Find the area enclosed by one loop ofthe four-leaved rose = . : / = /
  6. 6. Ex: Find the area enclosed by one loop ofthe four-leaved rose = . : / = / / = /
  7. 7. Ex: Find the area enclosed by one loop ofthe four-leaved rose = . : / = / / = / =
  8. 8. Ex: Find the are of the region that lies insidethe circle = and outside thecardioid = + .
  9. 9. Ex: Find the are of the region that lies insidethe circle = and outside thecardioid = + . :
  10. 10. Ex: Find the are of the region that lies insidethe circle = and outside thecardioid = + . : /= ( ) / / ( + ) /
  11. 11. Ex: Find the are of the region that lies insidethe circle = and outside thecardioid = + . : /= ( ) / / ( + ) /=
  12. 12. Arc length of a polar curve = ( )between = , =is given by = + O
  13. 13. Ex: Find the length of the cardioid = +
  14. 14. Ex: Find the length of the cardioid = += +
  15. 15. Ex: Find the length of the cardioid = += += ( + ) +
  16. 16. Ex: Find the length of the cardioid = += += ( + ) +=

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