chasityhainline7115 chasityhainline7115
  • 14-01-2020
  • Mathematics
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Find the volume of the solid of revolution formed by rotating the bounded region about the x-axis.
f(x)=4-x2, y=0, x=-1, x=1.

Respuesta :

LammettHash
LammettHash LammettHash
  • 14-01-2020

Use the disk method:

[tex]\displaystyle\pi\int_{-1}^1(4-x^2)^2\,\mathrm dx=2\pi\int_0^1(16-8x^2+x^4)\,\mathrm dx[/tex]

where we take advantage of symmetry to rewrite the limits, and expand the integrand.

[tex]=\displaystyle2\pi\left(16x-\frac83x^3+\frac15x^5\right)\bigg|_0^1=2\pi\left(16-\frac83+\frac15\right)=\frac{406\pi}{15}[/tex]

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