Question 1 (1 point)\ A solid is obtained by rotating the region bounded by

x=1,y=x^(3)

, and\ the

x

axis in the first quadrant (i.e.,

x>=0

) around the vertical line

x=2

.\ Using the method of rings, determine which of the following integrals represents the\ volume,

V

, of the solid.\

\\\\int_0^1 \\\\pi ((2-y^((1)/(3)))^(2)-1)dy\ \\\\int_0^1 \\\\pi ((y^((1)/(3)))^(2)-1)dy\ \\\\int_0^1 \\\\pi ((2-x^(3))^(2)-1)dx\ \\\\int_0^1 \\\\pi (1-y^((1)/(3)))^(2)dy

\

A solid is obtained by rotating the region bounded by x=1,y=x3, and the x axis in the first quadrant (i.e., x0 ) around the vertical line x=2. Using the method of rings, determine which of the following integrals represents the volume, V, of the solid. 01((2y1/3)21)dy01((y1/3)21)dy01((2x3)21)dx01(1y1/3)2dy