The value of the integral $I = \mathop \smallint \nolimits_0^1 \,x{\left( {1 - x} \right)^n}\,\;dx$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of the integral

I = \int \nolimits_0^1 \,x{\left( {1 - x} \right)^n}\,\;dx

View answer and explanation

Correct option: C

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

The correct answer is C (

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

) because it is the result of evaluating the definite integral using substitution or Beta function properties.

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I\,\,\left( {m,\,\,n} \right) = \int \nolimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} \right)^n}\,\,dt

I\left( {m,\,\,n} \right)

I\,\,\left( {m + 1,\,\,n + 1} \right)