#### To determine

**To describe:**

The solid

#### Answer

The solid is obtained by rotating the region bounded by y=2x and y=sinx, x=0 and x=π2 about line x=-1

#### Explanation

**1) Concept:**

By the shell method the volume of the solid by rotating the region under the curve y=f(x) about the line x=-1 from a to b is

V= ∫ab2π x+1 f(x)dx

where 0≤a≤b

**2) Given:**

∫0π22π x+1(2x-sinx)dx

**3) Calculations:**

The volume of the solid is

∫0π22πx+12x-sinx dx

The volume of the solid obtained by the revolution curve y=fx≥0 around the line x= axis in the interval (a, b) is

∫0π22π x-l2x-sinx dx

Comparing this volume with V= ∫ab2π x+1f(x)dx

where 0≤a≤b

∫0π22πx-l2x-sinx dx=∫ab2π(x+1)f(x)dx

Therefore,

fx=2x-sinx and line is x=-1

Therefore, the solid is obtained by rotating the region bounded by y=2x, y=sinx where 0≤x≤π2 about line is x=-1.

Alternatively, the solid is obtained by rotating the region bounded by y=2x and y=sinx, x=0 and x=π2 About line x=-1 as shown in figure.

**Conclusion:**

The solid is obtained by rotating the region bounded by y=2x and y=sinx, x=0 and x=π2 about line x=-1