Câu hỏi 47
Cho hàm tăng $f:[0,\pi/2]\to[0,\infty)$. Chứng minh:
a) $\displaystyle\int_0^{\pi/2}(f(x)-f(\pi/4))(\sin x-\cos x)\,dx\ge0$.
b) Tồn tại $a\in[\pi/4,\pi/2]$ sao cho $\displaystyle\int_0^a f(x)\sin x\,dx=\int_0^a f(x)\cos x\,dx$.
a) $\displaystyle\int_0^{\pi/2}(f(x)-f(\pi/4))(\sin x-\cos x)\,dx\ge0$.
b) Tồn tại $a\in[\pi/4,\pi/2]$ sao cho $\displaystyle\int_0^a f(x)\sin x\,dx=\int_0^a f(x)\cos x\,dx$.