Find the volume of the solid generated by revolving the region bounded by the parabola y² 4x and the line y = x about (a) the x-axis; (b) the y-axis; (c) the line x = 4; (d) the line y = 4. = 4.1 =

Find the center of mass of a thin plate covering the region bounded above by 2 the parabola y = 4 - x² and below by the x-axis. Assume the density of the plate at the point (x, y) is 8 = 2x², which is twice the square of the distance from the point to the y-axis.

find the area of the cylinder z=x+y2 that lies below the second-quadrant area bounded by x axis, x=-1, and y2=-x