1. Clicker Question 1 What is A. Converges to 4/5 B. Converges to -4/5
C. Converges to 1
D. Converges to 5
E. Diverges

2. Clicker Question 2 What is A. Converges to 1/10 B. Converges to -1/10
C. Converges to 1/5
D. Converges to ½ ln(5)
E, Diverges

3. Application: Arc Length (10/2/13)
What is the length of a given arc? More specifically, given the function f (x), how long is the curve of f as x goes from a to b? Call this length s.
Well, look at little short lengths s. By the Pythagorean Theorem, s  ((x)2 + (y)2)
Factoring out x and going to the limit we get

4. An Example of Arc Length
Find the arc length of f (x) = x 2 as x runs from 0 to 2.
The answer must be more than the straight line distance from (0,0) to (2,4), which is 25, or about
Well, which is a tough one!
So, use numerical integration: Simpson with n=2 gives (1 + 4(2) + 2(5) + 4(10) + 17) / 6 

5. Exact Answer?
Can we find the exact arc length of x2 from (0, 0) to (2, 4)?
This involves a trig sub followed by an integration by parts.
A careful, complete working through of this problem, showing the exact answer and its decimal approximation accurate to 4 decimal places, will get extra credit. (Due next Monday. Remember, extra credits are done ON YOUR OWN. No Googling, no help from anyone, etc. Honor Code!)

6. Clicker Question 3
Find the arc length of f (x) = (2/3) x 3/2 between x = 0 and x = 3.
A. 43 / 5
B. 21 / 2
C. 14 / 3
D. 16 / 3
E. 53 / 4

7. Assignment for Friday
Read Section 8.1 (omit, if you wish, the subsection on pages 541-3).
Do Exercises 1, 2, 3 (use Simpson’s Rule with n = 2), 7, and 13.