#### To determine

**To describe:**

The solid for an integral π∫1432-3-x2dx which represents the volume of a solid

#### Answer

= x, y| 1≤x≤4, 3-x≤y≤3 of the xy- planeabout the x- axis

#### Explanation

**1) Concept:**

i. If the cross section is a washer with inner radius rin and outer radius rout, then area of washer is obtained by subtracting the area of the inner disk from the area of the outer disk,

A=π outer radius2 -π inner radius2

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

V= ∫abA(x)dx

**2) Given:**

π∫1432-3-x2dx

**3) Calculation:**

Compare the given integral with expression for volume.

Thus we see that the cross section of the solid of volume the integral represents, is a washer with outer radius 3 and inner radius 3- x, and it is perpendicular to x- axis. So the axis of rotation is x-axis

So, the resulting solid is obtained by rotating the area bounded by the line y=3 and the curve y=3-x and it lies between x=1 and x=4, about the x-axis.

This can be written as

=x, y/1≤x≤4, 3-x≤y≤3

Therefore,

π∫1432-3-x2dx

describes the volume of the solid obtained by rotating the region

= x, y| 1≤x≤4, 3-x≤y≤3 of the xy- planeabout the x- axis

**Conclusion:**

π∫1432-3-x2dx

describes the volume of the solid obtained by rotating the region

= x, y| 1≤x≤4, 3-x≤y≤3 of the xy- planeabout the x- axis