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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 = += += ( + ) +=