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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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
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

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
∫(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)