Number six y=x^2 and the line y =2x for 0 inferior and equal to x inferior and equal to 2 That last part couldn't fit

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 (I)=V2x2 +1 and WP\": '1 IE [1, 3]. (Hint: Solids with Holes) (yZ + 2)]!2 3. Find the length of the curve x 3 from y = 0 to y = 3 4. Find the area of the surface generated by revolving about the x-axis the curve f\") = 2\"" on [1, 4]. 5. The spherical tank in Fig. 21 is full of water. How much work is done lifting the water to the top of the tank? Fig. 21 6. Calculate the centroid of the region (use Simpson's rule with n = 20 if necessary) a n n