Question
Asked Sep 18, 2019
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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

y=8x^3, y=0, x=1, about x=2

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Expert Answer

Step 1

Consider the given curves.

y 0
x 2
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y 0 x 2

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Step 2

Now, plot the curves on the x y planes:

10
10
x = 1
D
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10 10 x = 1 D

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Step 3

On rotating about the line x = 2, it gives a cylindrical shape with radius is 2 – x and h...

-27(2-x 8r)dt
-27f (16x -8&x* dc
16x 8r
=
27
4
5
16(1) 8(1)
= 27T
4
-(0)
5
8
= 27 4
5
12
27
5
24 units
5
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-27(2-x 8r)dt -27f (16x -8&x* dc 16x 8r = 27 4 5 16(1) 8(1) = 27T 4 -(0) 5 8 = 27 4 5 12 27 5 24 units 5

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