Calculus II - 18
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Stewart Calculus Section 10.4

Stewart Calculus Section 10.4

Statistics

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Calculus II - 18 Presentation Transcript

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