JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

, then the expression for

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

in terms of

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

View answer and explanation

Correct option: A

\frac{{{2^n}}}{{m + 1}}\,\, - \,\,\frac{n}{{m + 1}}\,\;I\left( {m + 1,\;\,n - 1} \right)

Option A (

\frac{{{2^n}}}{{m + 1}}\, - \,\frac{n}{{m + 1}}\,\;I\left( {m + 1,\;\,n - 1} \right)

) is correct because it is derived by integration by parts.

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