\( f:[0,1] \rightarrow R \) be a non increasing function, then for ...

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\( f:[0,1] \rightarrow R \) be a non increasing function, then for \( \alpha \in(0,1) \)
\( \mathrm{P} \)
(1) \( \alpha \int_{0}^{1} f(x) d x \leq \int_{0}^{\alpha} f(x) d x \)
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(2) \( \alpha \int_{0}^{1} f(x) d x \geq \int_{0}^{\alpha} f(x) d x \)
(3) \( \alpha^{2} \int_{0}^{1} f(x) d x \leq \int_{0}^{\alpha} f(x) d x \)
(4) \( \sqrt{\alpha} \int_{0}^{1} f(x) d x \geq \int_{0}^{\alpha} f(x) d x \)
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