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# Calculus II - 16

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Stewart Calculus Section 10.2

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### Calculus II - 16

1. 1. 10.2 Calculus with parametric Curves = ( ), = ()TangentsAreasArc LengthArea of Surfaces of Revolution
2. 2. Tangents:
3. 3. Tangents: If = , =
4. 4. Tangents: If = , = = =
5. 5. Tangents: If = , = = = !! =
6. 6. Areas: = ( ), = ( ),
7. 7. Areas: = ( ), = ( ), = () ()
8. 8. Ex: Find the area under the cycloid curve: = ( ), = ( ),
9. 9. Ex: Find the area under the cycloid curve: = ( ), = ( ), = [( )] · ( )
10. 10. Ex: Find the area under the cycloid curve: = ( ), = ( ), = [( )] · ( ) =
11. 11. Arc Length: = ( ), = ( ),
12. 12. Arc Length: = ( ), = ( ), = +
13. 13. Ex: Find the length of one arc of the cycloid curve: = ( ), = ( ),
14. 14. Ex: Find the length of one arc of the cycloid curve: = ( ), = ( ), = +
15. 15. Ex: Find the length of one arc of the cycloid curve: = ( ), = ( ), = + = ( )
16. 16. Ex: Find the length of one arc of the cycloid curve: = ( ), = ( ), = + = ( ) =
17. 17. Area of Surfaces of Revolution = ( ), = ( ),
18. 18. Area of Surfaces of Revolution = ( ), = ( ),If the curve is rotated about the x-axis: = +
19. 19. Area of Surfaces of Revolution = ( ), = ( ),If the curve is rotated about the x-axis: = +If the curve is rotated about the y-axis: = +
20. 20. Ex: Find the area of the surface obtained by rotatingthe arc of the cycloid curve about x-axis. = ( ), = ( ),
21. 21. Ex: Find the area of the surface obtained by rotatingthe arc of the cycloid curve about x-axis. = ( ), = ( ), = +
22. 22. Ex: Find the area of the surface obtained by rotatingthe arc of the cycloid curve about x-axis. = ( ), = ( ), = + = ( ) ( )
23. 23. Ex: Find the area of the surface obtained by rotatingthe arc of the cycloid curve about x-axis. = ( ), = ( ), = + = ( ) ( ) =