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