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Use cylindrical shells to find the volume of the solid generated when the region enclosed by the given curves is revolved about the y-axis.
y=x³,
x=1,
y=0

Respuesta :

LammettHash

Each shell has radius [tex]x[/tex] and height [tex]x^3[/tex], so the volume of this solid is

[tex]\displaystyle2\pi\int_0^1x^4\,\mathrm dx=\boxed{\frac{2\pi}5}[/tex]

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