Galaxy surveys show that x=dN/(dm d2); i.e., the number of galaxies per unit solid angle (in...

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Galaxy surveys show that x=dN/(dm d2); i.e., the number of galaxies per unit solid angle (in square degrees) and per unit magnitude increases with visual apparent magnitude (mv) as log10 X-0.35*my-4.4. a) Derive an expression for the total brightness (per square degree) of the night sky due to galaxies, in the range (m1, m2), assuming that the above relation holds for all magnitudes. b) Demonstrate explicitly that this converges at faint flux levels c) What is the total surface brightness (in mag/square degree and in mag/ asec2) contributed by galaxies in the magnitude range (+20,+30)? In the range (+15,+30)? Galaxy surveys show that x=dN/(dm d2); i.e., the number of galaxies per unit solid angle (in square degrees) and per unit magnitude increases with visual apparent magnitude (mv) as log10 X-0.35*my-4.4. a) Derive an expression for the total brightness (per square degree) of the night sky due to galaxies, in the range (m1, m2), assuming that the above relation holds for all magnitudes. b) Demonstrate explicitly that this converges at faint flux levels c) What is the total surface brightness (in mag/square degree and in mag/ asec2) contributed by galaxies in the magnitude range (+20,+30)? In the range (+15,+30)?