设所求积分为I,P'y=e^x cosy-my,Q=e^xcosy-m,P'y=-siny*e^x-m,Q'x=e^x*cosy,根据格林公式,I+∫[OA弧]=∮[OALO] [（e^x cosy-my)dx+(e^xcosy-m)dy]=∫[D}∫[e^x*cosy-(e^xcosy-m)]dxdy=m∫∫dxdy=m∫[0,π/4] ∫[0,co...