b)Consider the graph of y = (2x − x^2)^1/2 on the interval 0 ≤ x ≤ 2. Compute         the area of the surface of revolution formed by revolving this graph about the         x − axis.     c) Use a double integral to find the volume of the solid that is bounded above by         the plane z = 4 − x − y and below by the rectangle R = [0, 1] × [0, 2].

Suppose the solid W in the figure is the spherical half-shell consisting of the points above the xy-plane that are between concentric spheres centered at the origin of radii 4 cm and 10 cm. Suppose the density 8 of the material increases linearly with the distance from the origin, and that at the inner surface the density is 8 g/cm³ while at the outer surface it is 10 g/cm. (a) Using spherical coordinates, write d as a function of p. Enter p as rho. 8(e) = 25/9(rho-4) (5.0 (b) Set up the integral to calculate the mass of the shell in the form below. If necessary, enter o as phi, and 0 as theta. B D CLI 25/9(rho-4)rho^2sinphi "OP Ópdp A = 0 B = 2pi C = 0 D= pi/2 (Drag to rotate) E- 4 F= 10 (c) Find the mass of the shell. 4536pi

A trough, 10 ft long, has semi-elliptical ends which are 3 feet deep and 4 feet wide. If the trough is filled with water, what is the work done in pumping all the water out from the top of the trough? Find the volume of the solid generated by revolving the area bounded by the given curve y=lnx, x=e2, x-axis, about x=-e2

Find the area of the surface generated when the curve: a) y=(x^4)/8+1/(4x^2) on [1,2] is rotated about the x-axis. b) x=2sqrt(4-y), 0=<y=<15/4 is rotated about the y-axis.