设曲线弧L为x^2+y^2=ax(a>0)从点A(a,0)到点O(0,0)的上半圆弧,求∫(e^xsiny-ay+a)dx+(e^xcosy-a)dy

问题描述:

设曲线弧L为x^2+y^2=ax(a>0)从点A(a,0)到点O(0,0)的上半圆弧,求∫(e^xsiny-ay+a)dx+(e^xcosy-a)dy
∫下面有个L,e^xsiny是e^x乘以siny

补L1:y=0,x:0→a则L+L1为封闭曲线∮(L+L1) (e^xsiny-ay+a)dx+(e^xcosy-a)dy用格林公式=∫∫ (e^xcosy-e^xcosy+a) dxdy 积分区域D为半圆=a∫∫ 1 dxdy被积函数为1,积分结果为区域面积,面积为:(1/2)π(a/2)²=...