9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis. 


x = x³ ,y = 1, and x = 0; about the x-axis

Use the general slicing method to find the volume of the following solids.

The solid whose base is the triangle with vertices (0, 0), (2, 0), and (0, 2), and whose cross sections perpendicular to the base and parallel to the y-axis are semicircles

Use calculus to find the volume of a tetrahedron (pyramid with four triangular faces), all of whose edges have length 4.

Let f(x) = {x   if 0≤x≤2

      2x−2  if 2<x≤5

      −2x+18 if 5<x≤6. 

Find the volume of the solid formed when the region bounded by the graph of f, the x-axis, and the line x=6 is revolved about the x-axis.

Suppose the region bounded by the curve y=f(x) from x=0 to x=4 (see figure) is revolved about the x-axis to form a solid of revolution. Use left, right, and midpoint Riemann sums, with n=4 subintervals of equal length, to estimate the volume of the solid of revolution.

9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis. 

{Use of Tech} y = 1 / (x² + 1)²,y=0,x=1, and x=2; about the y-axis

9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis. 

{Use of Tech} y = √sin^−1x,y = √π/2, and x=0; about the x-axis

9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis. 

{Use of Tech} y = In x/x²,y = 0,x = 3, about the y-axis

9-34. Shell method Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about indicated axis. 

{Use of Tech} y = √50 -2x², in the first quadrant; about the x-axis