Could somebody walk through (step by step) the integral process for surface of revolution and solid of revolution for Gabriel's Horn?

I don't mean, explain it, I understand it .. I just keep getting a different expression for V of solid and my integration skills suck too much for me to get anywhere with the surface area expression even tho it appears to be relatively simple

I would love to, but I Failed calculus 1 and 2.

and I don't even know what you're talking about. I must have a high sperm count or something. O_o

I could tell you everything except the integration... which... is what you need.

It's the equation 1/x spun around the X-axis 3-dimensionally making a horn.
In lamans terms.

Volume of f(x) rotated around the X axis is pi*int(f(x)^2), aye? This is just conical area and the like. You ok on that point?

So, it's pi*int((1/x)^2)

which is pi*int(x^-2).

that is pi*((x^-1)/1), or just pi*-1/x.

The limits are a(any number>1) and 1.

Plugging that in, you get pi*(-1/a-(-1)), or just pi*(1-1/a)). I don't suppose that helps?

Oh, yeah, that does help for volume. I'm stupid and used sqrt(x) rather than 1/x for f(x) cuz I was thinking of another problem =/ .. eheh

Just to brush up on my crappy calc skills, I have some questions for lord kuat.

WHere did "pi*int(f(x)^2)," come from? That link pommy gave?

and how did you know to plug in 1/x for f(x)?

i might help you after my stats final

That just made me realize that Homer Simpson must...

Think of the cone as a bunch of slices on top of each other. Each of these slices is a circle. The area of a circle is pi*r^2. In this case, r=y. You are just moving the circle in space to form the cone. Thus pi*Int(r^2) = pi*int(y^2). Y(or f(x)) is defined by 1/x. Thus pi*int((1/x)^2). That answers both questions. You use an integral because you are trying to account for all the possible areas formed.

If I'm wrong, please correct me. In a forum full of computer scientists, possible engineers, ect, the medical student is giving math help. That just isn't right :p

(It's disk method for solid of revolution)