另询:∫L(x^2+y)dx+(2x-y^2)dy ,L是曲线 x^2+y^2=4x 的上半弧段
问题描述:
另询:∫L(x^2+y)dx+(2x-y^2)dy ,L是曲线 x^2+y^2=4x 的上半弧段
答
x^2 + y^2 = 4x ==> (x - 2)^2 + y^2 = 4若L是逆时针的话∫L (x^2 + y) dx + (2x - y^2) dy= ∫∫D [(2) - (1)] dxdy= ∫∫D dxdy= 4π若L是顺时针 ==> ∫L (x^2 + y) dx + (2x - y^2) dy = - 4π取L的上半圆 ==> y ...