**exact**volume of the solid by revolving the region about the line x=1.

my solution

I use the cylindrical method to solve the problem. The radius is r=1-x and the height is h=x^3+x+1.

Then, I integrate 2*pi*(1-x)(x^3+x+1) from the x-intercept on the negative side of the x-axis to 1.

Now, I have a problem. I don't know how to find the x-intercept.

The

**exact**value of the volume is

**43*pi/30**. Can someone explain how to determine the x-intercept? Thanks a lot.