Question

高等数学，请教一下打钩这题咋写？

Answer 1

如图所示：

Answer 2

1(1) P(x,y) = 2sin2xsin3y, P'<y> = 6sin2xcos3y
Q(x,y) = -3cos3ycos2x, Q'<x> = 6sin2xcos3y = P'<y>
u(x,y) = ∫ 2sin2xsin3ydx = -cos2xsin3y + g(y),
u'<y> = -3cos2xcos3y+g'(y) = Q(x,y) = -3cos3ycos2x
则 g'<y> = 0, g<y> = C,
则 u(x,y) = C-cos2xsin3y
2(1) P(x,y) = 6xy^2-y^3, Q(x,y) = 6x^2y-3xy^2,
Q'<x> = 12xy-3y^2 = P'<y>
该曲线积分与积分路径无关，选折线 A(1,2)B(3,2)C(3,4),
曲线积分 I = ∫<1,3>(24x-8)dx + ∫<2,4>(54y-9y^2)dy
= [12x^2-8x]<1,3> + [27y^2-3y^3]<2,4>
= 80+156 =236

追问

答非所问！