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Let R be the region bounded by the following curves. Use the shell method to find the volume of the solid generated when R is revolved about the x- axis.
y = Sqrt x , y = 0, and x = 81
V = ? (Type an exact answer in terms of pi)

Respuesta :

lublana

Answer:

[tex]V=47239.2\pi [/tex]

Step-by-step explanation:

We are given that

[tex]y=\sqrt{x}[/tex]

y=0

[tex]x=81[/tex]

When y=0 then x=0

Using shell method

Volume of solid

[tex]V=2\pi \int_{a}^{b}xf(x)dx[/tex]

Using the formula

Volume of solid

[tex]V=2\pi \int_{0}^{81} x(\sqrt{x})dx[/tex]

[tex]V=2\pi \int_{0}^{81}x^{\frac{3}{2}}dx[/tex]

[tex]V=2\pi [\frac{2}{5}x^{\frac{5}{2}}]^{81}_{0}[/tex]

[tex]V=2\pi\times \frac{2}{5}((81)^{\frac{5}{2}})[/tex]

[tex]V=47239.2\pi [/tex]