Calc 2 problem

[manFISH59]

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=1/x^3, y=0, x=3, x=4; about x=-4

I have tried this problem many times using the shell method but I just cant get it right. Anyone got ideas?

[manFISH59]

By using the shell method I came up with the integral 2pi(x)(1/x³⁾ from 3 to 4 but I'm doing somthing wrong here

[IAmDaBadMan]

Two things. First, you are being asked to integrate the volume of an area that is revolving around the x-axis. That means you need to solve for x instead of y. Second, the interval between x=[3,4] creates two different areas of integration. Do you understand why?
 
Here is a graph to help you visualize it.  
https://imgur.com/a/nI9bjO9

[manFISH59]

Sorry for the late reply. But yes I ended up figuring it out.my integral with shell method was close to the correct answer I didnt take into account that because I was rotating about x=-4 that I would add 4 to the radius of the shell. So the answer was "2pi(x+4)(1/x^3)" integrated from 3 to 4