# volumes of revolution ...help!!

#### oussama123443

Joined Nov 2, 2014
27
hey guys...!! what is the volume of the solid when rotating the areas between y=(x^3)-x and the x-axis around the line x=1 ???

#### djsfantasi

Joined Apr 11, 2010
7,693
Hey Oussama,
Does the solid extend into infinity? At what points along $$y=x^3-x$$ and $$x=0$$ (if at all) does the solid end?

#### oussama123443

Joined Nov 2, 2014
27
no boundaries were given for the integral , the function has x=1 and x=-1 as roots so i'm trying to figure if the shape generated will be from " -1 to 1"

#### WBahn

Joined Mar 31, 2012
26,398
hey guys...!! what is the volume of the solid when rotating the areas between y=(x^3)-x and the x-axis around the line x=1 ???
The bounds are definitely important and they are not at all obvious.

no boundaries were given for the integral , the function has x=1 and x=-1 as roots so i'm trying to figure if the shape generated will be from " -1 to 1"
What about the root at x=0?

I would recommend giving your answer in three parts. First, figure out the solid of revolution between each adjacent pairs of roots and then also give the sum of them. In addition, provide an explanation why you are using those limits as opposed to something even broader.

#### WBahn

Joined Mar 31, 2012
26,398
MOD NOTE: Moved to Homework Help from Math.