1. Length of Curves and Surface Area
Section 7.4

2. Length of Curves
Find the length of the curve 𝑦= 𝑥 2 from −1≤𝑥≤2.

3. Length of Curves
Find the length of the curve over the indicated interval:
𝑦= ln ( cos 𝑥) , 0, 𝜋 3

4. Length of Curves
Find the length of the curve over the indicated interval.
𝑥= 𝑦 𝑦−3 , 1≤𝑦≤4.

5. Surface Area
Find the surface area of the frustum:

6. Surface Area
Find the area of the surface formed by revolving the graph of 𝑓 𝑥 = 𝑥 3 on the interval x = 0, 1 about the x-axis.

7. Surface Area
Find the area of the surface formed by revolving the graph of 𝑓 𝑥 = 𝑥 2 on the interval 0≤𝑥≤ 2 about the y-axis.

8. Surface Area
Find the surface area of the surface generated by revolving the curve about the x-axis:
𝑦=2 𝑥 from 4≤𝑥≤9