Surface Area Equality: The Simplest Explanation

[calculushelp]

ok why does

surface area = ( y) ( 1+ f ' (x)^(2) )^(1/2)



equal


surface area = (x ) (1+ f ' (x)^(2) )^(1/2)



the simplest explanation please.

 

[Defennder]

Where did you get those formulae from? And surface area of what? You're supposed to do a surface integral in 3D space (the details of which depend on the parametrisation of the surface area)to get the surface area, but I don't see any integral sign. The formulae you gave resembles the one given for arc length calculation.

For a surface area of a function in 3D, for which the surface z(x,y) is given, the surface area of the portion that projects down onto a region R is given by $$\int \int_R \sqrt{\left(\frac{\partial z}{\partial x} \right)^2 + \left(\frac{\partial z}{\partial y}\right)^2 + 1} \ \ dA$$

 

[HallsofIvy]

ok why does

surface area = ( y) ( 1+ f ' (x)^(2) )^(1/2)



equal


surface area = (x ) (1+ f ' (x)^(2) )^(1/2)



the simplest explanation please.

There can be no explanation- what you have written makes no sense at all! Are there supposed to be integrals in there?
Are you talking about the area of surfaces of rotation?

 

[calculushelp]

yes! in rotation! sorry i didnt know how to put an integral sign.