How can the volume of a solid be found by rotating a region around a given line?

[regnar]

Find the volume of the solid obtained by rotating the region bounded by the given curves about the line y=1.

y = [tex]\sqrt[4]{x}[/tex] , y = xI couldn't figure out if a should subtract one from x or from y = [tex]\sqrt[4]{x}[/tex]. I don't know if I'm doing this right I tried subtracting it from x and got a negative area.
I also used this formula:
[tex]\pi[/tex][tex]\int[/tex]r^2 h

 

[Mark44]

Find the volume of the solid obtained by rotating the region bounded by the given curves about the line y=1.

y = [tex]\sqrt[4]{x}[/tex] , y = x


I couldn't figure out if a should subtract one from x or from y = [tex]\sqrt[4]{x}[/tex]. I don't know if I'm doing this right I tried subtracting it from x and got a negative area.



I also used this formula:
[tex]\pi[/tex][tex]\int[/tex]r^2 h

This formula is to be used when your typical volume element is a circular disk of radius r and thickness h. It is not at all applicable in this problem. Have you drawn a sketch of the region bounded by the two curves? Have you drawn a sketch of the solid generated when the region is rotated around the line y = 1? These sketches are necessary in helping you understand how to set up your integral. In this problem there are two approaches: cylindrical shells or circular washers.