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pishuonlain [190]
3 years ago
13

Y=x, y=0, y=4, x=6 : find the volume of the solid generated revolving around line x=6

Mathematics
1 answer:
Vilka [71]3 years ago
5 0
Using shells, the volume is

\displaystyle2\pi\int_0^6(6-x)x\,\mathrm dx

where 6-x is the distance from any point in the region along the x-axis to the axis of revolution x=6, which makes up the radius of each shell; and x is the height of each shell, which is determined by the line y=x.

So the volume is

\displaystyle2\pi\int_0^6(6x-x^2)\,\mathrm dx=2\pi\left(3x^2-\frac{x^3}3\right)\bigg|_{x=0}^{x=6}=72\pi
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