In my Calculus book, in the chapter that introduces multiple integration, it has a chapter on integrals that calculate the surface area of a function in space. They define the integral to be..(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int \int dS = \int \int \sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}dA [/tex]

However, one chapter later they have another chapter entitled "Surface Integrals" where they define the surface area of a function in space to be..

[tex] \int \int f(x,y,z) dS = \int \int f(x,y,g(x,y)) \sqrt{1+\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2}dA [/tex]

What is different between these two integrals? They both say they calculate surface area.

EDIT:

From what I can gather, the first one is for an area right under the function in space, and the second one is for a region other than the base under the curve. Is this correct?

Thanks!

~Matt

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# Difference between these two surface integrals?

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