# Constant Density

1. The area enclosed between and is revolved about the horizontal line to form a solid. Calculate the volume. ( Hint: Disks)

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2. Let R be the region between the graphs of f ( x) and gxon the given interval. Find the volume V of the solid obtained by revolving R about the x- axis , where

and [0, 4]. （ Hint: Solids with Holes）

3. Find the arc length of the curve over the interval [1, 8]

4. Find the length of the curve from = 0 to y = 3

5. Find the area of the surface generated by revolving about the x-axis the curve on .

6. Find the area of the surface generated by revolving about the x-axis the curve on .

7. Suppose that a spring has a natural length of 10 ft and that a weight of 100 lb is required to hold it compressed to a total length of 6 ft. How much work is required to stretch the spring from a total length of 15 ft to 25 ft?

10 ft 15ft 25ft

x = 0 x = 5 x = 15

8. Find , centroid of the region of constant density k covering the region bounded by the parabola and the line . (Hint: Find the intersections first, then find ).

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