We describe and demonstrate a technique that enhances the sensitivity of a spectrometer for trace gas detection by employing wavelength modulation spectroscopy (WMS) and integrating the absolute value of the recorded spectra across multiple lines of the species. The sensitivity is further enhanced by conducting WMS with large modulation depths. This technique is demonstrated using a continuously tunable external cavity CW quantum cascade laser to record the second harmonic wavelength modulated spectra of NO(2) across the peak of the R-branch from 1629.5 to 1633.9 cm(-1). By integrating the absolute value of the resulting spectra, the detection sensitivity of NO(2) is improved by a factor of 40 compared to the sensitivity achieved using single-line WMS with the same apparatus. By using this technique, we achieve a sensitivity of approximately 6 parts in 10(9) (ppb) using a short-path cell (a 1 m absorption cell with two passes).