设f(x)和g(x)在[a,b]上连续.试证:(∫abf(x)g(x)dx)2≤∫abf2(x)dx.∫abg2(x)dx.

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问题 设f(x)和g(x)在[a,b]上连续.试证:(∫abf(x)g(x)dx)2≤∫abf2(x)dx.∫abg2(x)dx.

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答案考虑[f(x)+λg(x)]2dx≥0.

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