f(x)二阶可导,f(x)为偶函数,f(0)=a≠0,f(x)'=1,则∫(0-a)xf''(x-a)dx =? ∫(0

学习 时间:2026-04-02 06:11:29 阅读:3667
f(x)二阶可导,f(x)为偶函数,f(0)=a≠0,f(x)'=1,则∫(0-a)xf''(x-a)dx =? ∫(0-a)是定积分,谢谢啦

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追寻的黄蜂

满意的画笔

2026-04-02 06:11:29

∫(0→a) xƒ''(x - a) dx= ∫(0→a) x d[ƒ'(x - a)]= xƒ'(x - a) |(0→a) - ∫(0→a) ƒ'(x - a) dx= aƒ'(0) - ƒ(x - a) |(0→a)= aƒ'(0) - ƒ(0) + ƒ(- a),ƒ'(0) = = a - a + ƒ(a)= ƒ(a)

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  • 简单的水壶
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    2026-04-02 06:11:29

    ∫(0→a) xƒ''(x - a) dx= ∫(0→a) x d[ƒ'(x - a)]= xƒ'(x - a) |(0→a) - ∫(0→a) ƒ'(x - a) dx= aƒ'(0) - ƒ(x - a) |(0→a)= aƒ'(0) - ƒ(0) + ƒ(- a),ƒ'(0) = = a - a + ƒ(a)= ƒ(a)

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