The region R is bounded by the x-axis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the x-axis.
3 answers
We've done a couple of these for you. You gonna show what you got, or just keep moochin'?
Here is what I have so far:
Radius = 1/(x^3)
Area of Cross Section = pi(1/(x^3))^2
Simplified: pi(1/(x^6))
Volume = (definite integral from 1 to 3) pi(1/(x^6))
= pi( -1 / 5(3)^5) - pi(-1 / 5(1)^5)
= pi (-1 / 1215) - pi (-1 / 5)
= pi(242 / 1215) = 0.625732858
Sincerely,
Mooch
Radius = 1/(x^3)
Area of Cross Section = pi(1/(x^3))^2
Simplified: pi(1/(x^6))
Volume = (definite integral from 1 to 3) pi(1/(x^6))
= pi( -1 / 5(3)^5) - pi(-1 / 5(1)^5)
= pi (-1 / 1215) - pi (-1 / 5)
= pi(242 / 1215) = 0.625732858
Sincerely,
Mooch
Very good-- perfect!
2 answers