#### 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≤2cosx

about x axis.

#### Explanation

**1) Concept:**

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

V=π∫0bf2xdx

**2) Given:**

∫0π22πcos2xdx

**3) Calculation:**

It is given that the volume of a solid is

∫0π22πcos2xdx

The volume of the solid obtained by revolution of curve y=fx≥0 around the x- axis in the interval 0, π2 is V=∫0bπf2(x)dx

Comparing this volume with V=∫0bπf2(x) dx

π∫0bf2(x)dx= π∫0π22cos2xdx

Therefore,

a=0, b=π2, f2x=2·cos2(x )

So,

fx=2cosx

The solid is obtained by rotating the region bounded by y=2cosx , 0≤x≤π2 about

x-axis.

Therefore, the solid is obtained by rotating the region

R=x,y⃒0≤x≤π2,0≤y≤2cosx about x axis.

**Conclusion:**

The solid is obtained by rotating the region

R=x,y⃒0≤x≤π2,0≤y≤2cosx about x axis.