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.

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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) = x⁻⁷ and the x-axis on the interval [ 1, ∞) is revolved about the x-axis.  

volume of the cubic units is π/13

Step-by-step 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