∫0Rdxln(1+x2+y2)dy(R＞0)．

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问题 ∫₀^Rdx

ln(1+x²+y²)dy(R＞0)．

选项

答案如图8．16所示． [*] I=[*]ln(1+x²+y²)dσ[*]dθ∫₀^Rln(1+r²)rdr [*] =[*][R²ln(1+R²)-R²+ln(1+²)] =[*][(1+R²)ln(1+R²)-R²]．

解析

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考研数学二

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