(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}xcdot int_a^b g(x)mathrm{\,d}x. ]
(2). 试证: [ cin (0,1)Rightarrow int_c^1 dfrac{e^t}{t}mathrm{\,d}t geq ecdot sinh(1-c). ]
(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}xcdot int_a^b g(x)mathrm{\,d}x. ]
(2). 试证: [ cin (0,1)Rightarrow int_c^1 dfrac{e^t}{t}mathrm{\,d}t geq ecdot sinh(1-c). ]