求 ∫(0到1)dx∫(x^2到 x)(2-x-y)dy
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∫[0,1]∫[x²,x] (2-x-y) dydx
= ∫[0,1] (2y-xy-y²/2)[x²,x] dx
= ∫[0,1] {[2(x)-x(x)-(x)²/2]-[2(x²)-x(x²)-(x²)²/2]} dx
= ∫[0,1] (2x-7x²/2+x³+x⁴/2) dx
= (x²-7/6*x³+x⁴/4+x^5/10)[0,1]
= (1-7/6+1/4+1/10) - 0
= 11/60
= ∫[0,1] (2y-xy-y²/2)[x²,x] dx
= ∫[0,1] {[2(x)-x(x)-(x)²/2]-[2(x²)-x(x²)-(x²)²/2]} dx
= ∫[0,1] (2x-7x²/2+x³+x⁴/2) dx
= (x²-7/6*x³+x⁴/4+x^5/10)[0,1]
= (1-7/6+1/4+1/10) - 0
= 11/60
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