Question

If $I\left( {m,\;\,n} \right) = \mathop \smallint \limits_0^1 \,{x^{m - 1}}{\left( {1 - x} \right)^{n - 1}}\,dx$, then

Accepted Answer

$I\left( {m,\;\,n} \right) = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^{m - 1}}}}{{{{\left( {1 + x} \right)}^{m + n}}}}\,\,dx = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^{n - 1}}}}{{{{\left( {1 + x} \right)}^{m + n}}}}\,\,dx$

Answer

$I\left( {m,\,\;n} \right) = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^m}}}{{{{\left( {1 + x} \right)}^{m + n}}}}\,\,dx = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^n}}}{{{{\left( {1 + x} \right)}^{m + n}}}}\,\,dx$

Answer

$I\left( {m,\;n} \right) = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^n}}}{{{{\left( {1 + x} \right)}^{m + n - 1}}}}\,\,dx = \mathop \smallint \limits_0^\infty \,\,\frac{{{x^m}}}{{{{\left( {1 + x} \right)}^{m + n - 1}}}}\,\,dx$

Answer

None of these

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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