Star formation history inferred using the dust corrections determined here (upper set of points; orange shaded region) and without those dust corrections (lower set of points; blue shaded region). These dust corrections (Table 5) are applied to the luminosity density determinations at z > 2 by Reddy & Steidel (2009), Bouwens et al. (2007, 2008). Otherwise, the dust corrections of Schiminovich et al. (2005) are assumed. The top panel is based upon the total UV luminosity density integrated to 0.3 L* _{z = 3} and the bottom panel is based upon the total UV luminosity density integrated to 0.04 L* _{z = 3} . The rest-frame UV continuum luminosity density is converted to a SFR density assuming a constant >10 ⁸ yr star formation model and a Salpeter (1955) IMF (Madau et al. 1998). Conversion to a Kroupa (2001) IMF would result in a factor of ~1.7 (0.23 dex) decrease in the SFR density estimates given here. Assuming younger ages for star-forming galaxies in high-redshift samples would increase the SFR density estimates by a similar factor (Verma et al. 2007). Shown are the luminosity density determinations by Schiminovich et al. (2005; black hexagons), Reddy & Steidel (2009; green crosses), Bouwens et al. (2007; blue/red circles), and Bouwens et al. (2008; blue/red circles and 1σ upper limit). The open symbols show the SFR densities that would be inferred if we applied the same dust correction to >0.04 L* _{z = 3} as we apply to >0.3 L* _{z = 3} . It is clear then that ignoring the fact that lower luminosity galaxies have much lower values for the dust extinction will result in an overestimate of the SFR density. See also Table 5. Table 5 and Figure 10 from Reddy & Steidel (2009) make a similar point. The equivalent SFR density (UV luminosity density) is also shown assuming no extinction correction (lower set of points).