设f(x)在[0.1]连续,证明∫(0→1)[f(x)^2]dx≥[∫(0→1)f(x)dx]^2
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设f(x)在[0.1]连续,证明∫(0→1)[f(x)^2]dx≥[∫(0→1)f(x)dx]^2
![设f(x)在[0.1]连续,证明∫(0→1)[f(x)^2]dx≥[∫(0→1)f(x)dx]^2](/uploads/image/z/7396076-20-6.jpg?t=%E8%AE%BEf%28x%29%E5%9C%A8%5B0.1%5D%E8%BF%9E%E7%BB%AD%2C%E8%AF%81%E6%98%8E%E2%88%AB%280%E2%86%921%29%5Bf%28x%29%5E2%5Ddx%E2%89%A5%5B%E2%88%AB%280%E2%86%921%29f%28x%29dx%5D%5E2)
本题证明有一定的技巧,下面给出两种证法,其中第二种证法需用到二重积分,如没学过二重积分,只看第一种证法即可.
![](http://img.wesiedu.com/upload/a/56/a56ed347a29f689dbc96d4a867284536.jpg)
![](http://img.wesiedu.com/upload/a/56/a56ed347a29f689dbc96d4a867284536.jpg)
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