#### To determine

**To describe:**

The solid

#### Answer

The solid is obtained by rotating the region bounded by x=y-1 , 1≤y≤5 about x-axis.

#### Explanation

**1) Concept:**

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

where 0≤a≤b.

**2) Given:**

∫152πy y-1dy

**3) Calculations:**

It is given that the volume of the solid is

∫152πy y-1dy

The volume of the solid obtained by the revolution curve x=gy≥0 around the x- axis in the interval a, b is

V= ∫ab2πy g(y)dy

Comparing this volume with ∫152πy y-1dy

∫152πy y-1dy=∫ab2πy g(y)dy

Therefore,

gy=x=y-1

Therefore, the solid is obtained by rotating the region bounded by x=y-1 , 1≤y≤5 about y-axis as shown below.

**Conclusion:**

The solid is obtained by rotating the region bounded by x=y-1 , 1≤y≤5 about x-axis.