1. An Interlude…

2. Arc Lengths and Surface Areas
How can we use a Riemann Sum to find the length of a curve?

3. Arc Length “s”
Example: what is the length along the parabola y = x2 from x = 0 to x = 2?

4. How about Surface Area?
Develop an expression for the surface area of the surface formed by rotating y = 1/x around the x-axis between x = 1 and x = 10
Generalize for all functions f(x), show that:

5. The strange case of “Gabriel’s Horn”
Which is bigger
The volume of revolution formed by rotating y = 1/x around the x-axis from x = 1 to infinity? or
The surface area formed by rotating y = 1/x around the x-axis from x = 1 to infinity?
Now, back to the salt mines!