The solid is obtained by rotating the region bounded by x=y-1 , 1≤y≤5 about x-axis.
i. By the shell method, the volume of the solid by rotating the region under the curve x=g(y) about x-axis from a to b is
V= ∫ab2πy g(y)dy
It is given that the volume of the solid is
The volume of the solid obtained by the revolution curve x=gy≥0 around the x- axis in the interval a, b is
Comparing this volume with ∫152πy y-1dy
∫152πy y-1dy=∫ab2πy g(y)dy
Therefore, the solid is obtained by rotating the region bounded by x=y-1 , 1≤y≤5 about y-axis as shown below.