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
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
