= Find the mass of the solid bounded by the the graphs of y 8x², y = 5, z = 0, and z = 2, in the first octant, if the density at a point P is equal to 6 times the distance to the yz-plane.

A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight density P Ibs./ft. The work (in ft-Ibs.) required to pump all the water over the upper rim is given by the integral (A 25лр (9-у) dy 25 (9-y)y? dy 81 (© 25xp (6-y)dy 25 81

Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top half of the circle x² + y² = 9. The mass density of 2 6 the wire is described by the function p(x, y) = xy. Find the total mass of the wire.

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.