Question

If $I\,\,\left( {m,\,\,n} ight) = \mathop \smallint 
olimits_0^1 \,\,{t^m}\,\,{\left( {1 + t} ight)^n}\,\,dt$,then the expression for $I\left( {m,\,\,n} ight)$ in terms of $I\,\,\left( {m + 1,\,\,n + 1} ight)$ is

Accepted Answer

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

Answer

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

Answer

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

Answer

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

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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