Pazopanib Hydrochloride, Paclitaxel, and Carboplatin in Treating Patients With Refractory or Resistant Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Peritoneal Cancer

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, fallopian tube, or peritoneal carcinoma * Recurrent disease * Received at least 1 prior platinum treatment and developed platinum-refractory disease (i.e., progression within 4 weeks of platinum administration) or platinum-resistant disease (i.e., progression within 6 months after the last platinum dose) * There is no restriction on the number of prior lines of treatment * Non-platinum treatment is allowed after proven platinum-resistance or -refractory disease * Evaluable (measurable or nonmeasurable) disease according to RECIST version 1.1 criteria * Patients with refractory disease on weekly paclitaxel and carboplatin regimen are excluded (phase II only) * No known gastrointestinal intraluminal metastatic lesions with risk of bleeding * No known endobronchial lesions and/or lesions infiltrating major pulmonary vessels * No known brain metastases or leptomeningeal disease PATIENT CHARACTERISTICS: * WHO performance status 0-2 * Absolute neutrophil count ≥ 1.5 x 10\^9/L * Hemoglobin ≥ 9 g/dL * Platelet count ≥ 100 x 10\^9/L * PT, aPTT, or INR ≤ 1.2 times upper limit of normal (ULN) * Total bilirubin ≤ 1.5 times ULN\* * ALT and AST ≤ 2.5 times ULN\* * Serum creatinine ≤ 1.5 mg/dL OR calculated creatinine clearance ≥ 50 mL/min * Urine protein creatinine ratio \< 1 OR 24-hour urine protein \< 1 g * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraceptio…