计算下列对坐标的曲线积分

2024-11-23 13:46:56
推荐回答(2个)
回答1:

回答2:

用高斯公式 ∯ x^2dydz + y^2z^2dzdx + z^2dxdy = 2 ∫∫∫ (x+yz^2+z)dxdydz = 2 ∫dz ∫dt ∫ (rcost+z^2*rsint+z)rdr = 2 ∫dz ∫dt [(1/3)r^3cost+(1/3)z^2*r^3sint+zr^2/2] = 2 ∫dz ∫ [(1/3)z^3cost+(1/3)z^5*sint+z^3/2]dt = 2 ∫dz [(1/3)z^3...