1. Areas and Volumes

2. Area of a circle

6. We need a substitution

7. Find the limit points

8. Replace

10. Volume of a sphere

11. Area of ellipse- use parametric equations

14. The Rings of the Lord w/2 r R

15. The Rings of the Lord Volume = w/2 r R

16. Volume = w/2 r R

17. Arc length

19. You need a substitution

21. A cable of length l is suspended between two towers of equal height a distance 2d apart, so that it sags a distance h in the centre. – The curve formed by a suspended rope or cable is called a catenary. Using a coordinate system with the lowest point of the catenary at the origin, it can be described by the equation – where a is a constant

22. Use the arc length formula to show that