1. The area enclosed between 37 = x2 + 1 and y = 2 is revolved about the horizontal line y = 2 to form a solid. Calculate the volume. (Hint: Disks) 2. Let R be the region between the graphs of f (x) and g(x) on the given interval. Find the volume V of the solid obtained by revolving R about the x- axis, where f(x) : x + 3 and g(x) = V3152 +1 x E [0, 4]. (m: Solids with Holes) 3. Find the arc length ofthe curve y = ix" + 2 over the interval [1, 8] (y: + 2)}!2 4. Find the length of the curve 1: = 3 fromy=0toy=3 5. Find the area of the surface generated by revolving about the x-axis the curve f(x)=2w.llxon [1,(}]. 1 6. Find the area of the surface generated by revolving about the x-axis the curve y = gxlon [0, v5] . 1'. 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 ? 10ft 15ft 25ft x=0 x=5 x=15 8. Find (1?), centroid of the region of constant density k covering the region bounded by the parabola y = 2x x2 and the line y = 2x . (Hint: Find the intersections rst, then nd M, f and 37, respectively}