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  3. 设f(x)＝求∫02xf(x－π)dx．

设f(x)＝求∫02xf(x－π)dx．

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问题 设f(x)＝求∫02xf(x－π)dx．
选项
答案∫02πf(x－π)dx＝∫02πf(x－π)d(x－π)＝∫－ππf(x)dx ＝∫－π0[sinx／(1＋cos2x)]dx＋∫0πxsin2xdx＝∫0πf(x－π)d(x－π)＝∫－ππf(x)dx ＝－π／2＋(π／2)×2∫0π／2sin2xdx＝－π／2＋π／2×2×(1／2)×(π／2)＝－π／2＋π2／4．
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考研数学一

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