Answer:

Explanation:
We are given that curves y=
is rotated about x=4 .
Given that y=0 and x=2
We have to find the volume V generated by rotating the region bounded by the curves with the help of method of cylindrical shells.
First we find the intersection point
Substitute y=0 then we get
0=

x=0
Hence, x changes from 0 to 2.
Radius =4-x
Height of cylinder =y=

Surface area of cylinder =

Volume V generated by the rotating curves
=

V=

V=
![2\pi[(12x^5)/(5)-(x^6)/(2)]^2_0](https://img.qammunity.org/2020/formulas/mathematics/high-school/h4fec4yze4xfktre110fwdxpj7gih945vq.png)
V=
![2\pi[(384)/(5)-32]](https://img.qammunity.org/2020/formulas/mathematics/high-school/3t04t6765wwmoeljyt2igti8ylrcokx53h.png)
V=


Hence, the volume V generated by rotating the region by the given curves about x =4=
.