1. 7.4 Length of a Plane Curve
y=f(x) is a smooth curve on [a, b] if f ’ is continuous on [a, b].

2. Where convenient, (3) can also be expressed as

3. Example Find the arc length of the curve from (1, 1) to
Solution:

4. Arc Length Formula for Parametric Curves

5. Example: Find the circumference of a circle of radius 2 from the parametric equations
Solution:

6. 7.5 Area of a Surface of Revolution
y=f(x) a b

7. Where convenient, S can also be expressed as

8. Example: Find the area of the surface that is generated by revolving the portion of
The curve between x=0 and x=1 about the x-axis.
Solution: Since , we have and hence the surface area S is