高等数学题目求解
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Ix = ∫∫<D>ρy^2dxdy = ∫<0, 2> dx ∫<-3√(x/2), 3√(x/2)> y^2dy
= 2∫<0, 2> dx ∫<0, 3√(x/2)> y^2dy = (2/3)∫<0, 2> dx [y^3]<0, 3√(x/2)>
= (2/3)[27/(2√2)]∫<0, 2> x^(3/2)dx = (9/√2)(2/5)[x^(5/2)]<0, 2> = 72/5
Iy = ∫∫<D>ρx^2dxdy = ∫<0, 2> x^2dx ∫<-3√(x/2), 3√(x/2)> dy
= 3√2∫<0, 2> x^(5/2)dx = 3√2(2/7)[x^(7/2)]<0, 2> = 96/7
= 2∫<0, 2> dx ∫<0, 3√(x/2)> y^2dy = (2/3)∫<0, 2> dx [y^3]<0, 3√(x/2)>
= (2/3)[27/(2√2)]∫<0, 2> x^(3/2)dx = (9/√2)(2/5)[x^(5/2)]<0, 2> = 72/5
Iy = ∫∫<D>ρx^2dxdy = ∫<0, 2> x^2dx ∫<-3√(x/2), 3√(x/2)> dy
= 3√2∫<0, 2> x^(5/2)dx = 3√2(2/7)[x^(7/2)]<0, 2> = 96/7
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