If \( f(x) \) is differentiable and \( \int_{0}^{t^{2}} x f(x) d x=\frac{2}{5} t^{5} \), then \(...

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If \( f(x) \) is differentiable and \( \int_{0}^{t^{2}} x f(x) d x=\frac{2}{5} t^{5} \), then \( f\left(\frac{4}{25}\right) \) equals
(A) \( 2 / 5 \)
(B) \( -5 / 2 \)
(C) 1
(D) \( 5 / 2 \)
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