1. Rita Korsunsky

2. Arc Length Formula: Let f be smooth(differentiable) on [a,b].
The arc length of the graph of f from A(a, f(a)) to
B(b, f(b)) is
f(x) a b

3. y B Q A
∆yk P
∆xk
Proof: x O a b

4. Example 1: If f(x) = 3x2/3 – 10, find the arc length of the graph of f from the point A(8,2) to B(27, 17).
f(x) = 3x2/3 – 10

5. Arc Length Formula:
(g(d),d)
x=g(y)
(g(c),c)

6. Example 2: Set up an integral for finding the arc length of the graph of the equation y3 – y – x = 0 from A(0,-1) to B(6,2).
x = y3 – y; c = -1, d = 2

7. Example 3: