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Find the volume of the described solid of revolution or state that it does not exist. The region bounded by ​f(x) and the​ x-axis on the interval ​[​,​) is revolved about the​ x-axis.

User Kaedys
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This question is incomplete, the complete question is;

Find the volume of the described solid of revolution or state that it does not exist.

The region bounded by ​f(x) = x⁻⁷ and the​ x-axis on the interval ​[ 1​,​ ) is revolved about the​ x-axis.

Answer: volume of the cubic units is π/13

Explanation:

Given that;

​f(x) = x⁻⁷

in the image, Area of ring = πR²

we substitute

Area = π (x⁻⁷)²

= π(x⁻¹⁴)

Now

Volume = ₁∫^∞ π(x⁻¹⁴) dx

= [ -π/13 x⁻¹³ ]₁^∞

= 0 + π/13

= π/13

therefore volume of the cubic units is π/13

Find the volume of the described solid of revolution or state that it does not exist-example-1
User Znik
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