Question

The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x3.
a.) Find the area of R.

b.) Find the value of h, such that the vertical line x = h divides the region R into two Regions of equal area.

c.) Find the volume of the solid generated when R is revolved about the x-axis.

d.) The vertical line x = k divides the region R into two regions such that when these two regions are revolved about the x-axis, they generate solids with equal volumes. Find the value of k.

Answer 1

*That is y = 1/x^3

Answer 2

Show me what you have done so far.
a) The first part especially should be very straight-forward. you should get 4/9

for the 2nd part, let the new vertical be x = h, so you have
2∫ (1/x^3) dx from 1 to h = ∫(1/x^3) dx from 1 to 3 , the last part you found in part a)

c) remember volume = π∫ y^2 dx from 1 to 3

d) follow the same logic I used in b)