曲线积分与曲面积分的问题∫L(e的x次siny-my)dx+(e的x次cosy-m)dy ,其中L为从A(a,0)到O(

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,cos2θ）rdrdθ
=mπa^2/8,
∵OA方程为y=0,
dy=0,
∫[OA](e^x cosy-my)dx+(e^xcosy-m)dy=0,
∴I=πma^2/8,