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sinx/x和(sin(x^2))/x^2在零到正无穷上的对应的广义积分值相等,如何论证?
人气:318 ℃ 时间:2020-06-29 20:05:27
解答
(0,+∞)∫(sinx/x)^2dx=(1/2)*(0,+∞)∫(1-cos2x)/x^2dx=(1/2)*(0,+∞)∫1/x^2dx-(1/2)*(0,+∞)∫cos2x/x^2dx=(1/2)*(0,+∞)∫1/x^2dx-(1/2)*(0,+∞)∫cos2x/d(1/x)=(1/2)*(0,+∞)(-1/x)-(1/2)*(0,+∞)cos2x/x+(1/2)...
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