1.The area enclosed between y = x² and y = 4 is revolved about the horizontal line y = 4 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)= 2x²+ 1 and g(x)=x²-1 x [1, 3]. (Hint: Solids with Holes)

3. Find the length of the curve x= (y²+2)^3/2 / 3 from y = 0 to y = 3

4. Find the area of the surface generated by revolving about the x-axis the curve f (x) = 2 x 1 on [1, 4].

5. The spherical tank is full of water. How much work is done lifting the water to the top of the tank? radius =4ft

6. Calculate the centroid of the region (use Simpson's rule with n = 20 if necessary) y = x² and the line y = 2x for 0 x 2.