Let's do some calculus! (20)

Calculus Level 4

limn(k=1nak1(k1)akaf(x)f(x)+f((2k1)ax) dx)=75\lim_{n \to \infty} \left(\sum_{k=1}^n a^{k-1} \int_{(k-1)a}^{ka} {\dfrac{f(x)}{f(x) + f \left( \left(2k-1\right)a-x \right)}} \ dx \right) = \dfrac{7}{5}

Given that function f(x)>0f(x) > 0,  xR\forall ~ x \in \mathbb{R} is bounded and satisfies the condition above. If a<1a < 1, find aa.


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