#### To determine

**To describe:**

The solid for the integral π∫01y4-y8dy which represents the volume of a solid

#### Answer

= x, y/0≤y≤1,y4≤x≤y2, about the y- 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 y-axis is

V= ∫abA(y)dy

**2) Given:**

π∫01y4-y8dy

**3) Calculation:**

Comparing the below integral with expression for volume,

π∫01(y2)2-(y4)2dy

We see that the cross section of the solid of which the above integral gives volume, is a washer with outer radius y2 and inner radius y4 and cross section is perpendicular to the axis of rotation y axis.

So, the solid is obtained by rotating the area bounded by the curve x= y4 and the curve x= y2 and it lies between y=0 and y=1 about y-axis.

This can be written as

=x, y/0≤y≤1,y4≤x≤y2

Therefore, the givenintegral describes the volume of the solid obtained by rotating the region

= x, y/0≤y≤1,y4≤x≤y2 of the xy- plane about the y- axis

**Conclusion:** The integral

**π∫01y4-y8dy**

describes the volume of the solid obtained by rotating the region

= x, y/0≤y≤1,y4≤x≤y2 of the xy- plane about the y- axis