Question

The Region R is bounded by the x-axis, x=1, x=3, and y=1/x^3.

Answer 1

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 2

@FaiqRaees

Answer 3

@zepdrix

Answer 4

This is as far as I got \[\pi \int\limits_{1}^{k}(\frac{ 1 }{ x ^{2} })^{2} dx = \pi \int\limits_{k}^{3}(\frac{ 1 }{ x ^{3} })^{2}dx\]

Answer 5

both of the denominators are supposed to be x^3

Answer 6

Hmm looks good so far :)
Divide the pi's,\[\large\rm \int\limits\limits_{1}^{k}\frac{1}{x^6}dx = \int\limits\limits_{k}^{3}\frac{1}{x^6}dx\]then expand out the integrals and solve for k.

Answer 7

okay

Answer 8

i got here

Answer 9

ok let's divide the -1/5 out of each side.
It just makes it easier to plug everything in if they're not floating around.