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计算二重积分步骤,计算二重积分,写步骤解释

∫(-1→2)dx∫(x2-2→x2+1)x(x2-y)dy=∫(-1→2)dx∫(x2-2→x2+1)(x3-xy)dy=∫(-1→2)(x3y-?xy2)|(y=x2-2→x2+1)dx=∫(-1→2)[x3(x2+1)-?x(x2+1)2]-[x3(x2-2)-?x(x2-2)2]dx=∫(-1→2)[(x^5+x3-?x^5-x3-?x)-(x^5-2x3-?x^5+4x3-4x)]dx=...

∫(-1→2)dx∫(x2-2→x2+1)x(x2-y)dy =∫(-1→2)dx∫(x2-2→x2+1)(x3-xy)dy =∫(-1→2)(x3y-?xy2)|(y=x2-2→x2+1)dx =∫(-1→2)[x3(x2+1)-?x(x2+1)2]-[x3(x2-2)-?x(x2-2)2]dx =∫(-1→2)[(x^5+x3-?x^5-x3-?x)-(x^5-2×3-?x^5+4×3-4x)]dx =∫(-1→2)[-2×3+(7/2)x]dx =[-?x^4+(7/4)x2]|(x=-1→2) =[-?×16+(7/4)×4]-[-?×1+(7/4)×1] =(-8+7)-(5/4) =-9/4

计算二重积分步骤,计算二重积分,写步骤解释插图

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