#### To determine

**To describe:**

The solid given by the integral

#### Answer

The solid is obtained by rotating the region

R=x,y⃒0≤x≤π2,0≤y≤cosx about y axis.

#### Explanation

**1) Concept:**

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

V= ∫ab2πxf(x)dx

where, 0≤a≤b

**2) Given:**

∫0π22πxcosxdx

**3) Calculation:**

It is given that the volume of a solid is

∫0π22πxcosxdx

The volume of the solid obtained by revolution curve y=fx≥0 around y- axis in the interval 0, π2 is given by V=∫ab2πxf(x)dx

Comparing this with V=∫0π22πxcosxdx

We have

∫0π22πxcosxdx=∫ab2πxf(x)dx

Therefore,

a=0, b=π2, fx=cosx

The solid is obtained by rotating the region bounded by y=cosx , 0≤x≤π2 about

y-axis.

Therefore, the solid is obtained by rotating the region

R=x,y⃒0≤x≤π2,0≤y≤cosx about y axis.

**Conclusion:**

The solid is obtained by rotating the region

R=x,y⃒0≤x≤π2,0≤y≤cosx about y axis.