#### To determine

**To describe:**

The solid for an integral π∫0πsinxdx which represents the volume of a solid

#### Answer

= x, y| 0≤x≤π, 0≤y≤sinx. Rotation about the x- axis

#### Explanation

**1) Concept:**

i. If the cross section is a disc and the radius of the disc is in terms of x or y, then area A=π radius2

ii. The volume of the solid revolution about the x-axis is

V= ∫abA(x)dx

**2) Given:**

π∫0πsinxdx

**3) Calculation:**

Given π∫0πsinxdx can be written as π∫0πsinx2dx

Compare this with expression for volume.

So the given expression is the volume of a solid with cross section a disc with radius sinx, and it is perpendicular to the axis of rotation x- axis.

So, the solid is obtained by rotating the area bounded by the line y=0 and the curve y= sinx, between x=0 and x=π about the x-axis.

This region can be written as

= x, y| 0≤x≤π, 0≤y≤sinx

Therefore, the integral

π∫0πsinxdx

describes the volume of the solid obtained by rotating the region

= x, y| 0≤x≤π, 0≤y≤sinx of the xy- plane about the x- axis

**Conclusion:**

π∫0πsinxdx

The above integral describes the volume of the solid obtained by rotating the region

= x, y| 0≤x≤π, 0≤y≤sinx of the xy- planeabout the x- axis