Q59 / 150 · MHT CET 2020 (19 Oct Shift 1) · Mathematics

$\int_{0}^{1} x(1-x)^{5} d x=$

  • A
    $\frac{1}{7}$
  • B
    $-\frac{1}{42}$
  • Correct answer
    C
    $\frac{1}{42}$
  • D
    $\frac{1}{6}$

Solution

(C) $\begin{aligned} \text { Let } I &=\int_{0}^{1} x(1-x)^{5} d x \\ \therefore I &=\int_{0}^{1}(1-x)(1-(1-x))^{5} d x=\int_{0}^{1}(1-x) x^{5} d x=\int\left(x^{5}-x^{6}\right) d x \\ &=\left[\frac{x^{6}}{6}-\frac{x^{7}}{7}\right]_{0}^{1}=\frac{1}{6}-\frac{1}{7}=\frac{1}{42} \end{aligned}$

Hence, the correct answer is option: 'C'.

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