#### To determine

**To find:**

The volume generated by rotating the region R2 about the line BC by using the figure.

#### Answer

V=π15

#### 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 the area A=π radius2

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

V= ∫abA(y)dy

**2) Given:**

**Figure:**

**3) Calculation:**

Rotating R2 about BC that is about line y=1.

Rotating R2 about BC that is the line y=1, the cross section is perpendicular to the x-axis and it is a disc with the radius r=1-x4. Because it is the distance from the curve y= x4 to the axis of the rotation line BC (y=1)

The solid lies between x=0 and x=1.

V=∫01πr2 dx

V= ∫01π1-x42 dx

V= ∫01π1-2x4+xdx

V= πx-2·45x54+23x3210

V=π1-85+23-0=π15

Therefore, the volume generated by rotating the region R2 about the line BC is

V=π15

**Conclusion:**

The volume generated by rotating the region R2 about the line BC is

V=π15