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I have this integral

[tex]

\int_0^{2\pi}\int_0^\pi \mathbf A\cdot\hat r d\theta d\phi

[/tex]

where [itex]\hat r[/itex] is the position unit vector in spherical coordinates and [itex]\mathbf A[/itex] is a constant vector. Is it possible to evaluate this integral without calculating the dot product explicitly, i.e. without knowing that that [itex]\hat r=(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta) [/itex] ?

Thanks.

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# Spherical coordinates surface integral

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