1. Arc Length and Surface Area
Lesson 10.8
The Sequel

2. Using Parametric Equations
Recall formula for arc length
If x = f(t) and y = g(t) it can be shown that

3. Example Given x = sin t, y = cos t Determine dx/dt and dy/dt
What is the arc length from t = 0 to t = 2π
Determine dx/dt and dy/dt
dx/dt = cos t dy/dt = -sin t
Now what is the integral?

4. Using Polar Equations Given a curve in polar form r = f (θ)
Must have continuous first derivative on interval
Curve must be traced exactly once for a ≤ θ ≤ b
Arc length is

5. Try it Out! Given polar function Find dr/dθ
What is the arc length from θ = 0 to θ = 4
Find dr/dθ
What is the integral and its evaluation

6. Surface Area – Parametric Form
Recall formula for surface area of rectangular function revolved about x-axis
Formula for parametric form about x-axis
Change this to x if revolved about y-axis

7. Surface Area Example Given x = t, y = 4 – t2 from t = 0 to t = 2
Surface area if revolved around x-axis

8. Surface Area – Polar Form
Curve revolved around x-axis
Curve revolved around y-axis

9. Find That Surface Area Given r = sin θ, θ = 0 to θ = π/2
Revolve about polar (x) -axis

10. Assignment
Lesson 10.8
Page 451
Exercises 1 – 21 odd