简单计算一下即可，答案如图所示
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第1个回答 2020-04-25
∫∫ |x^2+y^2-1|dxdy
=∫dx∫(1-x^2-y^2)dy+∫dx∫(x^2+y^2-1)dy
=2/3∫(1-x^2)^(3/2)dx+2/3∫(1-x^2)^(3/2)dx+(1/3)∫dx+∫(x^2-1)dx
=-1/3+4/3∫(1-x^2)^(3/2)dx【令x=sint】
=-1/3+4/3∫ (cost)^3×cost dt
=-1/3+4/3∫(cost)^4 dt
=-1/3+4/3×3/4×1/2×π/2
=π/4-1/3本回答被网友采纳
=∫dx∫(1-x^2-y^2)dy+∫dx∫(x^2+y^2-1)dy
=2/3∫(1-x^2)^(3/2)dx+2/3∫(1-x^2)^(3/2)dx+(1/3)∫dx+∫(x^2-1)dx
=-1/3+4/3∫(1-x^2)^(3/2)dx【令x=sint】
=-1/3+4/3∫ (cost)^3×cost dt
=-1/3+4/3∫(cost)^4 dt
=-1/3+4/3×3/4×1/2×π/2
=π/4-1/3本回答被网友采纳