The value of the integral $\mathop \smallint \limits_0^1 \,\,x{\left( {1 - x} \right)^n}\,\,dx$, is

$\frac{1}{{n + 1}}\,\, + \,\,\frac{1}{{n + 2}}$

$\frac{1}{{n + 2}}\,\, - \,\,\frac{1}{{n + 1}}$

$2\,\,\left( {\frac{1}{{n + 1}}\,\, - \,\,\frac{1}{{n + 2}}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The value of the integral

\int \limits_0^1 \,\,x{\left( {1 - x} \right)^n}\,\,dx

, is

View answer and explanation

Correct option: B

\frac{1}{{\left( {n + 1} \right)\,\,\left( {n + 2} \right)}}

Option B (

\frac{1}{{\left( {n + 1} \right)\,\,\left( {n + 2} \right)}}

) is correct because after applying the property of definite integrals and simplifying, we arrive at this result.

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