设正值函数f(x)在[0,1]上连续,试证:e^(

设正值函数f(x)在[0,1]上连续,试证:e^(∫(0→1)lnf(x)dx)

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设f(x)在[0,1]上连续且可导,又f(0)=0,0≤f'(x)≤1 试证：[ ∫^(0,1)f(x)dx]^2≥∫^
设 f'(x)在[0,1]上连续,试求∫[1+x f'(x)]e^ f'(x)dx ( 范围是0到1)
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设函数f(x)在闭区间[0,1]上连续,又设f(x)只取有理数,且f(1/2)=2,试证在闭区间[0,1]上,f(x)恒
f(x)在[0,1]连续,(0,1)内可导,满足f(0)=∫(0→1)e^(-x)f(x)dx,证：存在ξ∈(0,1),
设函数f(x)在x=0点连续,且f(0)=0,已知|g(x)|≤|f(x)|,试证函数g(x)在x=0点也连续
设f(x)在[0,1]上连续,证明[∫(0,1)f(x)dx]^2
1.函数f(x)在[0,1]连续,在（0,1）上可导,且f(0)=f(1)=0,f(1/2)=1,试证：