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Triple Integral in Spherical Coordinates 
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Sep1504, 04:18 AM

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I have a hemispherical surface of radius R with it's base centred on the origin. We are using the convention:
r is the radius i.e. the magnitude of the position vector of a point: its distance from the origin. theta is the polar angle phi is the azimuthal angle I am asked to calculate the integral of the divergence of a given vector field v over this volume (enclosed by the hemisphere). So far what I have done is to say that a full sphere would be given by the equation: r = R What about a hemisphere? It seems to me that the angle theta must be restricted so that points below the xy plane are not part of the domain. So what are the allowed values of theta? I can't seem to figure out whether it should be pi/2 < theta < pi/2, or something else? I need to know this to set my bounds of integration for one of the three integrals. Thanks. 


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