Integrating dP/dr over the Sun

[CaptainEvil]

Homework Statement

Consider the Sun to be a sphere of hydrogen gas of uniform density equal to its
average density (1440 kg/m3).
a) Integrate the equation of hydrostatic equilibrium for dP/dr from the Sun’s radius to the
core to estimate the central pressure in Pa and in atmospheres. Assume the pressure at the
surface is zero. [Note: your estimate will fall far short of the true value that can be
derived using a more realistic density profile, about 250 billion atmospheres, but that’s ok
for our purposes]

Homework Equations

dP/dr = -Gmp/r^2 (p = density)

The Attempt at a Solution

I replaced m with 4/3pir^3p which yields
dP/dr = -4piGrp^2/3
and integrated from R to 0 yielding 2piGp^2R^2/3
and filling in the values and Radius of the sun, I get 1.4e6 atm of pressure.
Does this make sense? (Is it consistent with what the question is asking)

 

[CaptainEvil]

bump - need help please