A lamina occupies the part of the disk $ x^2 + y^2 \le 1 $ in the first quadrant. Find its center of mass if the density at any point is proportional to its distance from the x-axis.
In Exercises $1-6,$ use the shell method to find the volumes of the solids generated by revolving the shaded region about the indicated axis.
Find the volumes of the solids.The solid lies between planes perpendicular to the $x$ -axis at $x=-1$ and $x=1 .$ The cross-sections perpendicular to the $x$ -axis are circular disks whose diameters run from the parabola $y=x^{2}$ to the parabola $y=2-x^{2}.$
Find the volumes of the solids.The solid lies between planes perpendicular to the $x$ -axis at $x=-1$ and $x=1 .$ The cross-sections perpendicular to the $x$ -axis between these planes are squares whose diagonals run from the semicircle $y=-\sqrt{1-x^{2}}$ to the semicircle $y=\sqrt{1-x^{2}}.$
