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≥∫^
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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≥∫^(0,1)[f(x)]^3dx
虽然想从0≤f'(x)≤1入手说明f(x)>[f(x)]^3,但貌似没什么用
虽然想从0≤f'(x)≤1入手说明f(x)>[f(x)]^3,但貌似没什么用
![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≥∫^](/uploads/image/z/1456777-1-7.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5B0%2C1%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%E4%B8%94%E5%8F%AF%E5%AF%BC%2C%E5%8F%88f%280%29%3D0%2C0%E2%89%A4f%27%28x%29%E2%89%A41+%E8%AF%95%E8%AF%81%EF%BC%9A%5B+%E2%88%AB%5E%280%2C1%29f%28x%29dx%5D%5E2%E2%89%A5%E2%88%AB%5E)
两边同时求导
或相减后求导
或相减后求导
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≥∫^
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