Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the​ y-axis.

y equals 8 left parenthesis 1 plus 8 x squared right parenthesis Superscript negative 1y=81+8x2−1​,

yequals=​0,

xequals=​0,

and

xequals=2

20xy

y equals StartFraction 8 Over 1 plus 8 x squared EndFractiony=81+8x2

Upper RR

A coordinate system has a horizontal x-axis labeled from 0 to 2 plus and an unlabeled positive vertical y-axis. From left to right, a curve labeled y equals StartFraction 8 Over 1 plus 8 x squared EndFraction starts on the positive y-axis and falls at an increasing and then decreasing rate in quadrant 1. As x approaches positive infinity, the curve approaches the x-axis from above. A dashed vertical line segment extends from the x-axis at 2 to the curve. The region above the x-axis, to the right of the y-axis, below the curve, and to the left of the vertical line segment is shaded and labeled R.

Question content area bottom

Part 1

Set up the integral that gives the volume of the solid using the shell method. Use increasing limits of integration. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Type exact​ answers.)