The exclusive reaction γp→pπ+π− was studied in the photon energy range 3.0–3.8 GeV and the momentum transfer range 0.4<−t<1.0  GeV2. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. In this kinematic range, the integrated luminosity was about 20  pb−1. The reaction was isolated by detecting the π+ and proton in CLAS, and reconstructing the π− via the missing-mass technique. Moments of the di-pion decay angular distributions were derived from the experimental data. Differential cross sections for the S, P, and D-waves, in the Mπ+π− mass range 0.4–1.4 GeV, were derived performing a partial wave expansion of the extracted moments. Beside the dominant contribution of the ρ(770) meson in the P-wave, evidence for the f0(980) and the f2(1270) mesons was found in the S and D-waves, respectively. The differential production cross sections dσ/dt for individual waves in the mass range of the above-mentioned mesons were extracted. This is the first time the f0(980) has been measured in a photoproduction experiment.