Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

Let J_n= ₀^ / 2 (1- x)^n 2 x d x . Find _ n=0 ^ J_n .

Correct answer

Step-by-step solution

Put x=t aligned J_n & = ₀^1 t(1-t)^n d t=2( ₀^1(1-t)^n d t- ₀^1 (1-t)(1-t)^n _ (1-t)^ n+1 d t) & =2 ( ₀^1 t^n d t- ₀^1 t^ n+1 d t )=2 ( 1 n+1 - 1 n+2 ) aligned aligned _ n=0 ^ J_n & =2 _ n=0 ^ ( 1 n+1 - 1 n+2 ) & =2(1)=2 aligned

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