Recent content by crox

Sorry, when I read it again I saw that it is unclear: f(z) is any function, that depends on z - for example: x^2+y^2=(z-1)^2 - this is some given function. In the case of f(y, z) I just wanted to stress the dependence and f(y, z) serves only as an abbreviation.

back again (thanks Mark44 for fas reply), but I still have questions. Let's say that I have a surface defined by x^2+y^2=f(z) or rewritten x=\pm\sqrt{f(z)-y^2}=f(z, y). The formula for surface area is in this case: P=\int\int\sqrt{ (\frac{\partial f(y, z)}{\partial y})^2+(\frac{\partial f(y...

I'd have one more question regarding this sphere example - how could I rigorously calculate the surface area? If I got the formula correctly, this could be done with: http://en.wikipedia.org/wiki/Area - general formula (bottom of the page) again in the case of sphere: f(x...

Thanks, Mark. @Char. Limit Yes, it would be easier in this case, but not in general (sphere served only as an example)

Homework Statement calculating volume under a surface, defined by implicit function f(x, y, z)=0 (in cartesian coordinates, strictly not in polar). Because the function that i need to integrate is quite complicated and there would be no obvious way to double check the result i first tried to...