怎么判断一个式子是不是瑕积分 瑕积分的敛散性怎么判断??大概步骤是怎样的
\u600e\u4e48\u5224\u65ad\u7455\u79ef\u5206\u7684\u7455\u70b9\u3001\u9ebb\u70e6\u8bf4\u7684\u901a\u4fd7\u4e00\u70b9\u3001\u6bd4\u5982\u8bf4\u4e0b\u9762\u8fd9\u9053\u9898\uff1f\u600e\u4e48\u770b\u51fa\u6765\u7455\u70b9\u662f0\uff1f\u8bbe\u51fd\u6570f(x)\u5728[a,b]\u4e0a\u9664\u70b9c(a<c<b)\u5916\u8fde\u7eed\uff0c\u70b9c\u4e3af(x)\u7684\u7455\u70b9\u3002
\u663e\u7136f(x)\u5728x=0\u5904\u4e0d\u8fde\u7eed
\u5173\u4e8e\u7455\u79ef\u5206\u655b\u6563\u6027\u7684\u5224\u522b,\u901a\u5e38\u7684\u5224\u522b\u6cd5\u6bd4\u8f83\u5355\u4e00,\u53c8\u7531\u4e8e\u5224\u522b\u6cd5\u672c\u8eab\u7684\u5c40\u9650\u6027,\u4f7f\u8bb8\u591a\u7455\u79ef\u5206\u7684\u655b\u6563\u6027\u96be\u4ee5\u5224\u5b9a\u3002\u9009\u62e9\u5408\u9002\u7684\u5224\u522b\u6cd5\u5bf9\u4e8e\u65e0\u7a77\u9650\u7455\u79ef\u5206\u7684\u655b\u6563\u6027\u6765\u8bf4\u663e\u5f97\u975e\u5e38\u91cd\u8981\u3002
ju\u4e2a\u4f8b\u5b50:\u222b0\u52301 dx/\u4e09\u6b21\u6839\u53f7\u4e0b(x(e^x-e^-x)\u7684\u655b\u6563\u6027\u5982\u4f55\u5224\u65ad?
\u89e3:
x->0\u65f6,e^x-e^(-x) -> (1+x)-(1-x) = 2x
\u4e8e\u662f\u539f\u5f0f\u53d8\u6210 dx/((2x^2)^(1/3)) = 2^(-1/3) * x^(-2/3) dx
\u4e8e\u662f\u6536\u655b\u3002
判断一个积分是否为瑕积分关键看在积分区间上有没有函数无界的点,如果有,一定要把区间在瑕点处分开进行积分。
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