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∫0到3/2dx∫0到3-2x（3x-2y)dy
题目详情
∫0到3/2 dx∫0到3-2x （3x-2y)dy
▼优质解答
答案和解析
∫0到3/2 dx∫0到3-2x （3x-2y)dy
=∫0到3/2[3x(3-2x)-(3-2x)^2]dx
=∫0到3/2[(5x-3)(3-2x)]dx
=∫0到3/2(-10x^2+21x-9)dx
=(-10/3x^3+21/2x^2-9x)|(0,3/2)
=-45/4+63/4-27/2
=-9
=∫0到3/2[3x(3-2x)-(3-2x)^2]dx
=∫0到3/2[(5x-3)(3-2x)]dx
=∫0到3/2(-10x^2+21x-9)dx
=(-10/3x^3+21/2x^2-9x)|(0,3/2)
=-45/4+63/4-27/2
=-9
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