12.设函数f(x)连续，且满足f(x)=e^x+int_(0)^xtf(t)dt-xint_(0)^xf(t)dt，求f(x).

6.设函数φ(x)连续，且满足varphi(x)=e^x+int_(0)^xtvarphi(t)dt-xint_(0)^xvarphi(t)dt,求φ(x).6

设f(x)可微，且满足=(int )_(0)^xf(t)dt+(int )_(0)^xtf(t-x)dt，则f(x)=．设f(x)可微，且满足，则f(x)=．

[题目]-|||-设连续函数f(x)满足 (x)=(e)^x+(int )_(0)^x(t-x)f(t)dt 求f(x).

[例18] 设f(x)连续,试求下列函数的导数.-|||-(1) (int )_({e)^x}f(t)dt;-|||-(2) (int )_(0)^x(x-t)

设f(x)是连续函数,且 (x)=(x)^2+2(int )_(0)^2f(t)dt 则 f(x)=设f(x)是连续函数,且 (x)=(x)^2+2(int )

[例18]设f(x )连续,试求下列函数的导数.-|||-(1)f(t)dt;-|||-(2) (int )_(0)^x(x-t)f(t)dt ;-|||-(3

9.设函数f(x)连续, (x)=(int )_(0)^sin xf(t(x)^2)dt-|||-(1)求F`(x);-|||-(2)讨论函数F`(x )的连续

[例8.24] 求连续函数f(x),使它满足 (x)+2(int )_(0)^xf(t)dt=(x)^2,

设 gt 0 时 f(x)可导,且满足 (x)=1+dfrac (1)(x)(int )_(1)^xf(t)dt, 求 f(x).

设f(x)连续,且 (x)=x+2(int )_(0)^1f(t)dt, 则 f(x)= __