Problem about int

ngocduy1842

[这个贴子最后由ngocduy1842在 2013/12/26 10:13pm 第 1 次编辑]

Function f(x) and g(x) is positive, continuous on [a,b]. Prove that, for all $\alpha \in \mathbb{R}$, have a number $c \in (a,b)$ that:
$$\dfrac{f(c)}{\int_a^c f(x) dx}-\dfrac{g(c)}{\int_c^b g(x) dx} = \alpha$$