[Everyday Mathematics]20150101
2015-01-01 14:30
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(1). 设 $f(x),g(x)$ 在 $[a,b]$ 上同时单调递增或单调递减, 试证: \[ (b-a)\int_a^b f(x)g(x)\mathrm{\,d}x \geq \int_a^b f(x)\mathrm{\,d}x\cdot \int_a^b g(x)\mathrm{\,d}x. \]
(2). 试证: \[ c\in (0,1)\Rightarrow \int_c^1 \dfrac{e^t}{t}\mathrm{\,d}t \geq e\cdot \sinh(1-c). \]
(2). 试证: \[ c\in (0,1)\Rightarrow \int_c^1 \dfrac{e^t}{t}\mathrm{\,d}t \geq e\cdot \sinh(1-c). \]
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