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4 years ago

Multiple Choice

Mathematics

1 answer:

inessss [21]4 years ago

5 0

Answer:
B
Step-by-step explication:
(1/4)/(3/8)=(2/3)

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Question Part Points Submissions Used Use the method of cylindrical shells to find the volume V generated by rotating the region

pochemuha

Answer:

$V=\frac{448\pi}{5}$

Step-by-step explanation:

We are given that curves y= $3x^4$ 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= $3x^4$

x=0

Hence, x changes from 0 to 2.

Radius =4-x

Height of cylinder =y= $3x^4$

Surface area of cylinder = $2\pi r h$

Volume V generated by the rotating curves

= $2\pi\int_{0}^{2} (4-x)(3x^4)dx$

V= $2\pi\int_{0}^{2}(12x^4-3x^5)dx$

V= $2\pi[\frac{12x^5}{5}-\frac{x^6}{2}]^2_0$

V= $2\pi[\frac{384}{5}-32]$

V= $2\pi\frac{384-160}{5}$

$V=\frac{448\pi}{5}$

Hence, the volume V generated by rotating the region by the given curves about x =4= $\frac{448\pi}{5}$ .

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4 years ago