So today I finished up the method that I was describing in the last post. What I had initially started to do was to approximate the curves to get an equation that I could then integrate. Instead what I realized would be easier and probably more accurate was to just use a trapezoidal approximation since I was given lots of data points. After getting the area under each curve, I then multiplied it by the flux density for the respective filter and added them up. I then converted the flux here at the Earth to the flux near the star. I ended up getting some mixed results. On the one hand it gave a very good approximation for the inner boundary for the star Proxima Centauri(.025 Au compared to other estimates of .023), but it does not give good estimates for the outer boundary for Proxima Centauri or another star Tau Centi.
I have many theories as to why the estimation is so poor, but I mainly think that it is a combination of the fact that the current estimates of the habitable zones for these stars were probably calculated with a different(most likely more complex) method and that our model seems to be very sensitive to small changes in data which would mean small errors in magnitudes measured by the telescopes could have a large impact. The other thing that it may be is the flux requirement I found for the outer boundary might be wrong. When I used the current estimate of the habitable zones I found the flux to be (290 and 410 W/m^2) at the outer edge of the zone. The fact that these numbers are so close might indicate that the 960 W/m^2 boundary I initially found might be incorrect and that it is in fact much lower. This has become the goal for tomorrow: to check more sources about how much flux is needed for the inner and outer boundary of the habitable zone.