\(\int_0^1 x(1-x)^5\,dx=\)
A. \(\frac{1}{56}\)
B. \(\frac{1}{42}\)
C. \(\frac{1}{6}\)
D. \(\frac{1}{30}\)
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Answer: B. \(\frac{1}{42}\)
Using \(x\to1-x\): \(\int_0^1(1-x)x^5dx=\frac16-\frac17=\frac1{42}\).
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· 23 Oct 2026
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