1. Section 9.1 Arc Length and Surface Area I
MAT 1235 Calculus II
Section 9.1
Arc Length and Surface Area I

2. HW…
WebAssign 9.1I

3. Preview
Derive the formula for the length of a segment of a curve.

4. Arc Length

5. Riemann Sum, Definite Integral
Any limit of the form :
can be interpreted as

6. Quote...
“Formula come, formula go – they’ll drift in and out of your life, almost like characters in a favorite book. When you finally close the cover, the characters have told their story and you start up again with another book, complete with new characters and adventures. Then you find yourself focusing on the new ones, not the ones from the past.”

7. Arc Length

8. Arc Length

9. Recall: The Mean Value Theorem
Let 𝑓 be a function satisfies the following conditions:
1. 𝑓 is continuous on the closed interval [𝑎,𝑏].
2. 𝑓 is differentiable on the open interval (𝑎,𝑏).
Then there is a number 𝑐 in (𝑎,𝑏) such that
or, equivalently,

10. The Mean Value Theorem a c b

11. Arc Length

12. Arc Length

13. Example 1
Find the length of the curve

14. Arc Length (second formula)

15. Bonus Problem
You may get bonus points for submitting a type up solutions of this problem.
Must be your own work, do not Google.
There are at least 3 different solutions.
Find the length of the curve

16. Classwork Work with your team partner only.
Do not “announce” your answer/solution.