Final answer:
The question involves using the shell method in integral calculus to find the volume of a solid of revolution, generated by revolving the region bounded by given curves around the y-axis.
Step-by-step explanation:
The subject of this question is Mathematics, specifically focusing on the application of integral calculus to find the volume of a solid of revolution using the shell method. To find the volume of the solid generated when the region r is revolved about the y-axis, one must set up an integral that calculates the volume of concentric cylindrical shells. These cylindrical shells have a radius x, height (1/x2), and thickness dx. The formula to find the volume V of each cylindrical shell is V = 2π • (radius) • (height) • (thickness), and hence the volume of the solid is calculated by integrating from x=0 to x=2. Since we are revolving around the y-axis, the height of each shell is given by the function y = 1/x2.
To find the volume, we integrate: Volume = ∫ 2_0 2πx(⅔1x2)dx. This evaluates to 2π ∫ 2_0 (⅔1x)dx, which can be simplified and calculated to find the volume of the solid.