Q:  What are the values of these two integrals?


         The first integral, over phi, has value      =   2 pi

         The second integral, over theta, has value   =   2



  Q:  What is the value of the entire right-hand-side?


          We end up with

                                  1
             mean intensity  =   ----  *  I_lambda *  ( 2 * 2 pi )
                                 4 pi


              < I_lambda >   =    I_lambda


          which is a rather nice result for isotropic radiation fields.