Do Now: #16 on p.518

1. Do Now: #16 on p.518 Find the length of the curve. Evaluate numerically…

2. Surface Areas of Parametrized Curves Section 10.1b

3. Surface Area (from a Smooth Parametrized Curve) If a smooth curve , , , is traversed exactly once as increases from to , then the areas of the surfaces generated by revolving the curve about the coordinate axes are as follows. 1. Revolution about the x-axis : 2. Revolution about the y-axis :

4. The standard parametrization of the circle with radius 1 centered at the point (0, 1) in the xy-plane is Use this parametrization to find the area of the surface swept out by revolving the circle about the x-axis (look at Figure 10.4 on p.517).

5. The standard parametrization of the circle with radius 1 centered at the point (0, 1) in the xy-plane is Use this parametrization to find the area of the surface swept out by revolving the circle about the x-axis (look at Figure 10.4 on p.517).

6. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. y-axis Graph the curve and visualize the surface…

7. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. y-axis

8. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. y-axis

9. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. x-axis Graph the curve and visualize the surface…

10. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. x-axis

11. Guided Practice Find the area of the surface generated by revolving the curve about the indicated axis. x-axis