高等数学，第5题怎么做？
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D ： (y-3)/2 ≤ x ≤ (3-y)/2, 0 ≤ y ≤ 3
总质量 M = ∫∫<D> ydxdy = ∫<0, 3> ydy ∫<(y-3)/2, (3-y)/2> dx
= ∫<0, 3> y(3-y)dy = ∫<0, 3> (3y-y^2)dy
= [3y^2/2-y^3/3]<0, 3> = 9/2 .
∫∫<D> xydxdy = ∫<0, 3> ydy ∫<-(3-y)/2, (3-y)/2> xdx = 0.
∫∫<D> yydxdy = ∫<0, 3> y^2dy ∫<-(3-y)/2, (3-y)/2> dx
= ∫<0, 3> y^2(3-y)dy = ∫<0, 3> (3y^2-y^3)dy
= [y^3-y^4/4]<0, 3> = 27/4 .
则 质心横坐标 x = 0， 纵坐标 y = (27/4)/(9/2) = 3/2
总质量 M = ∫∫<D> ydxdy = ∫<0, 3> ydy ∫<(y-3)/2, (3-y)/2> dx
= ∫<0, 3> y(3-y)dy = ∫<0, 3> (3y-y^2)dy
= [3y^2/2-y^3/3]<0, 3> = 9/2 .
∫∫<D> xydxdy = ∫<0, 3> ydy ∫<-(3-y)/2, (3-y)/2> xdx = 0.
∫∫<D> yydxdy = ∫<0, 3> y^2dy ∫<-(3-y)/2, (3-y)/2> dx
= ∫<0, 3> y^2(3-y)dy = ∫<0, 3> (3y^2-y^3)dy
= [y^3-y^4/4]<0, 3> = 27/4 .
则 质心横坐标 x = 0， 纵坐标 y = (27/4)/(9/2) = 3/2
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