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JEE Previous Year Question

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

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

A $1/5$
B $1/42$
C $1/13$
D $13/42$

Correct answer: B

Solution

(b) : Let I = \int_{0}^{1} x (1 - x)^{5} dx = - \int_{0}^{1} (1 - x - 1) (1 - x)^{5} dx = - (\int_{0}^{1} (1 - x)^{6} dx - \int_{0}^{1} (1 - x)^{5} dx) = \int_{0}^{1} (1 - x)^{5} dx - \int_{0}^{1} (1 - x)^{6} dx = (\frac{( 1 - x ) ^{6}}{- 6})_{0}^{1} - (\frac{( 1 - x ) ^{7}}{- 7})_{0}^{1} = \frac{1}{6} - \frac{1}{7} = \frac{1}{42}

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