用极坐标求积分求解答 求问定积分用极坐标的算法是怎么求的，麻烦给出详细过程谢谢！
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dxdy=rdrdθ这是又面积元得到的
考虑极坐标r = r(θ)在θ和θ＋dθ范围内围成的扇形圆环面积
ds = 1/2 * (r+dr)^2 * dθ - 1/2 * r^2 * dθ = r * dr * dθ (忽略掉dr^2*dθ)
所以dxdy = ds = rdrdθ
极坐标x = rcosθ ,y = rsinθ
所以x^2+y^2=r^2
所以对r的积分为r*e^(-r^2/2)*r
然后按照普通方式积分就可以了
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绛旓細鏋佸潗鏍鏂圭▼锛歳=acos胃 ds=鈭歔r²+(r')²]d胃=鈭(a²cos²胃+a²sin²胃)d胃=ad胃 鈭 鈭(x²+y²) ds =a鈭玔-蟺/2鈫捪/2] r d胃 =a²鈭玔-蟺/2鈫捪/2] cos胃 d胃 =a²sin胃 |[-蟺/2鈫捪/2]=2a²
