# Surface integral problem.

1. Dec 6, 2012

### countzander

1. The problem statement, all variables and given/known data

Consider the surface S formed by rotating the graph of y = f(x) around the x-axis between x = a and x = b. Assume that f(x) ≥ 0 for axb. Show that the surface area of S is 2π times integral of f(x)sqrt(1 + f ' (x)^2) dx from a to b.

http://i.imgur.com/qFeGP.png

2. Relevant equations

The integral of the magnitude of the cross product of the partial derivatives of parameterization vector, r = r(s,t). The region is R.

3. The attempt at a solution

I tried parameterizing the surface with parameters of x and f(x). The surface I set as g(x,f(x)). But when I took the cross product of that thing, I ended up with a useless statement involving partial derivatives which does not lead to the solution.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Dec 6, 2012
2. Dec 7, 2012

### haruspex

That's not an equation. Can you elaborate?
Please post details of you working.

3. Dec 7, 2012

### tiny-tim

hi countzander!
why so complicated?

just use trig!

(and f' = tan)

4. Dec 7, 2012

### countzander

http://i52.photobucket.com/albums/g12/countzander/Untitled-1.png [Broken]

Last edited by a moderator: May 6, 2017
5. Dec 7, 2012

### LCKurtz

That isn't two parameters. $x$ is free to use as a parameter but then $f(x)$ is determined. You need another parameter if you want to do it that way. I would suggest $\theta$, the angle of rotation as the second parameter. Express your surface as$$\vec R(x,\theta) = \langle x, ?, ?\rangle$$where the question marks are the appropriate expressions for $y$ and $z$ in terms of $x,\, f(x),\, \theta$.