记Ω(R)={(x,y)|x2+y2≤R2},求dxdy;

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问题 记Ω(R)={(x,y)|x2+y2≤R2},求dxdy;

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答案首先用极坐标变换求出I(R)=[*]dxdy,然后求极限[*]I(R). 作极坐标变换X=rcosθ,y=rsinθ得 [*] 因此,[*]dxdy=π.

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