Question

Use the disk method or the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line.y =10/ x² ,y = 0,x = 1,x=5

a) the x-axis
b) the y-axis
c) the line y = 10

Answer 1

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line, use the Disk Method or the Shell Method.

Step-by-step explanation:

To find the volume of the solid generated by revolving the region bounded by the graphs of the equations about each given line, we can use the Disk Method or the Shell Method.

• For part (a) where we need to revolve the region about the x-axis, we will use the Disk Method. We will integrate from x = 1 to x = 5 and use the formula V = π ∫[a, b] (f(x))² dx, where f(x) = 10/x².
• For part (b) where we need to revolve the region about the y-axis, we will also use the Disk Method. We will integrate from y = 0 to y = 10 and use the formula V = π ∫[a, b] (g(y))² dy, where g(y) is the inverse function of f(x) = 10/x².
• For part (c) where we need to revolve the region about the line y = 10, we will use the Shell Method. We will integrate from x = 1 to x = 5 and use the formula V = 2π ∫[a, b] x(f(x) - h(x)) dx, where f(x) = 10/x² and h(x) = 10.