When doing surface integrals of surfaces described parametrically, we use the area element(adsbygoogle = window.adsbygoogle || []).push({}); dA=ndS = (rx_{v}r)dvdw_{w}

Where dS is the surface area element and v and w are the parameters.

I'm fine with the derivation of this (I think) but I don't understand why it's necessary to havenand dS together, as in not just make an expression fornand dS seperately.

I think I'm misunderstanding something because I thoughtn=rx_{v}rbecause this is a vector perpendicular to_{w}rand_{v}rtherefore perpendicular to the surface. But then if this were true, according to the equation for_{w}dAat the top that would make dS = dvdw, which isn't necessarily true e.g. if v and w are polars.

Thanks

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# Area element vector for parametric surface integrals

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