(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The planar region bounded by [itex]y = x, y = \sqrt{x}[/itex] is rotated about the line x = -2.

Find the Volume.

2. Relevant equations

[itex]V = 2\pi\int_{0}^{4} R dA[/itex]

3. The attempt at a solution

Solution:

y = -2

(-2)^2 = x

x = 4

y^2 = +- 2

the point of intersection should be (0,0) and (4,2)

now im using the cylindrical method in obtaining the volume

[itex]V = 2\pi\int_{0}^{4} R dA[/itex]

where dA = (y2-y1)dx

for

y2 = sqrt(x)

y1 = x

and

radius be r = x+2 since the revolved line is at the 2nd quadrant and x in the 1st quadrant and it needs to be added

[tex]V = 2\pi\int_{0}^{4} (x+2)(y_{2}-y_{1}) dx [/tex]

[tex]V = 2\pi\int_{0}^{4} (x+2)(\sqrt{x}-{x}) dx [/tex]

V = -(416/15)pi ????

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# Volume using integral

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