同济高三课后习题有详细解答吗？

(1)薄皮质量M = ∫∫u(x，y)dxdy

= ∫dy∫(x+2y)dx

= ∫dy[x^2/2+2yx]

= ∫(2+2y-4y^2)dy =[2y+y^2-4y^3/3]= 5/3。

(2)薄板质量中心的坐标:

横坐标=(1/M)∫∫徐(x，y)dxdy

= (3/5)∫dy∫x(x+2y)dx

= (3/5)∫dy[x^3/3+yx^2)

= (3/5)∫[8/3-2y^2-(2/3)y^3]dy

=(3/5)[8y/3-(2/3)y^3-(1/6)y^4)

= (3/5)(11/6)=11/10

纵坐标= (1/M)∫∫yρ(x，y)dxdy

= (3/5)∫dy∫y(x+2y)dx

= (3/5)∫ydy[x^2/2+2yx)

= (3/5)∫y(2+2y-4y^2)dy

= (3/5)∫y(2+2y-4y^2)dy

=(3/5)[y^2+2y^3/3-y^4)=(3/5)(2/3)= 2/5

切片质心坐标(11/10，2/5)