Question

请大神帮我做一道高数题，关于曲面积分的

Answer 1

解：P=x/(x^2+y^2+z^2)^(3/2) Q=y/(x^2+y^2+z^2)^(3/2) R=z/(x^2+y^2+z^2)^(3/2)
偏P/偏x=1/(x^2+y^2+z^2)^(3/2)-3x^2/(x^2+y^2+z^2)^(5/2)
偏Q/偏y=1/(x^2+y^2+z^2)^(3/2)-3y^2/(x^2+y^2+z^2)^(5/2)
偏R/偏z=1/(x^2+y^2+z^2)^(3/2)-3z^2/(x^2+y^2+z^2)^(5/2)
偏P/偏x+偏Q/偏y+偏R/偏z=3/(x^2+y^2+z^2)^(3/2)-3(x^2+y^2+z^2)/(x^2+y^2+z^2)^(5/2)=0
∴根据高斯公式：∫∫Pdydz+Qdzdx+Rdxdy=∫∫∫( 偏P/偏x+偏Q/偏y+偏R/偏z)dxdydz=0