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We know that surface integrals come to the form of a surface integral of a scalar function over a surface and a vector field over a surface. First one is [tex]\oint F(x,y,z)d{S}[/tex] and the second one is [tex]\oint \vec{F}(x,y,z)\cdot d\vec{S}=\oint \vec{F}(x,y,z)\cdot \vec{n}dS[/tex], where [itex]n[/itex] is the unit normal vector of surface [itex]S[/itex].

Lately, I've seen integrals of the form [tex]\oint \vec{p}dp[/tex], over [itex]p[/itex], where [itex]p[/itex] is a unit vector. I fail to understand the meaning of that, is it surface integral of scalar or vector function? There is no dot product if its a vector function, so what am i missing here?

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# Confusing Surface Integral

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