Let R be the region below y=1/(x^(2/3)), above the x-axis and to the right of x = 1. Note that this region is not bounded.
(a) Show that the area of R is unbounded.
(b) Show that the volume of R rotated about the x-axis is bounded and find the volume.
I figured out part (a), but i still don't know how the area R is bounded after rotating about x-axis.

Question

Let R be the region below y=1/(x^(2/3)), above the x-axis and to the right of x = 1. Note that this region is not bounded.
(a) Show that the area of R is unbounded.
(b) Show that the volume of R rotated about the x-axis is bounded and find the volume.
I figured out part (a), but i still don't know how the area R is bounded after rotating about x-axis.

anonymous · Answer

Here is the graph i draw, it still looks unbounded after rotation
|dw:1362022901201:dw|