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\( 4 \lim _{n \rightarrow \infty} n \int_{0}^{\pi / 2}(1-\sqrt[n]{\sin x}) d x \) equals (A) \( \pi \ln 2 \) (B) \( \frac{\pi}{2} \ln 2 \) (C) \( -\frac{\pi}{2} \ln 2 \) (D) none

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