[All Steps] Let f be continuous on $[a, b] .$ Suppose that ∫_a^x f=∫_x^b f for all x ∈ [a, b]. Prove that f(x)=0 for all x ∈ [a,


Question: Let \(f\) be continuous on $[a, b] .$ Suppose that \(\int_{a}^{x} f=\int_{x}^{b} f\) for all \(x \in[a, b]\). Prove that \(f(x)=0\) for all \(x \in[a, b]\)

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