\(-\frac{2}{H^{2}\ \sqrt{\pi}}\int_{\frac{\text{A\ }}{\sqrt{t_{0}}}}^{\frac{\text{A\ }}{\sqrt{t_{f}}}}{\ e^{-w^{2}}\text{\ dw}}=-\frac{2}{H^{2}\ \sqrt{\pi}}\left(\int_{\frac{\text{G\ }}{\sqrt{t_{0}}}}^{\infty}{\ e^{-w^{2}}\text{\ dw}}-\int_{\frac{\text{G\ }}{\sqrt{t_{f}}}}^{\infty}{\ e^{-w^{2}}\text{\ dw}}\right)\)
\(=-\frac{2}{H^{2}\ \sqrt{\pi}}\left[\frac{\sqrt{\pi}}{2}\text{erfc}\left(\frac{G}{\sqrt{t_{0}}}\right)-\frac{\sqrt{\pi}}{2}\text{erfc}\left(\frac{G}{\sqrt{t_{f}}}\right)\right]\)
\(=-\frac{1}{H^{2}}\left[\text{erfc}\left(\frac{G}{\sqrt{t_{0}}}\right)-\text{erfc}\left(\frac{G}{\sqrt{t_{f}}}\right)\right]\) (35)