If ∫ 0 1 x m ( 1 - x ) n d x = k ∫ 0 1 x n ( 1 - x ) m d x , then the value of k equals

Question

If &#8747; 0 1 x m ( 1 - x ) n d x = k &#8747; 0 1 x n ( 1 - x ) m d x , then the value of k equals

Aicharya · Accepted Answer

G i v e n : &#160; &#8747; 0 1 &#160; 1 - x n x m d x = k &#8747; 0 1 &#160; x n &#160; 1 - x m d x &#8658; I ( m , n ) = &#8747; 0 1 &#160; x m &#160; 1 - x n d x &#8658; &#8747; 0 a &#160; f x d x = &#8747; 0 a f a - x d x &#8658; I ( m , n ) = &#8747; 0 1 &#160; 1 - x m &#160; 1 - 1 - x n d x &#8658; I ( m , n ) = &#8747; 0 1 &#160; 1 - x m &#160; 1 - 1 + x n d x &#8658; I ( m , n ) = &#8747; 0 1 &#160; 1 - x m &#160; x n d x &#8658; k = 1

If &#8747; 0 1 x m ( 1 - x ) n d x = k &#8747; 0 1 x n ( 1 - x ) m d x , then the value of k equals

Solution

If ∫ 0 1 x m ( 1 - x ) n d x = k ∫ 0 1 x n ( 1 - x ) m d x , then the value of k equals