Surface area in spherical co-ordinates

[FleetFoot]

I have a generalised function in spherical polar co-ordinates that describes the radiant intensity in any given direction of a point source emitter. I need to calculate the fraction of the total radiation that is emitted into a region of space specified by some min to max range of elevation angles phi and a min to max range of azimuth angles theta.

I know that the solution to the problem is essentially finding the surface area of the function by a double integration over phi and theta. However although I know how to solve a generalised surface integral in cartesian co-ordinates I'm not getting anywhere trying to solve this is spherical co-ordinates. Any help would be appreciated.

 

[mathman]

dxdydz=r²drducosvdv, where r is the radial direction, u is "longitude" (full circle), and v is "latitude" (-π/2 < v < π/2). You could replace cosvdv by sinwdw for 0 < w < π.