Most Important Selected Qs for JEE AdvancedMathematicsDefinite Integration

If I_n= ₀^ e^ -x ( x)^n d x(n 1) , then the value of 101 I₁₀ 10 I₈ is equal to

Correct answer

Step-by-step solution

I_n= ( e^ -x ( x)^n -1 )₀^ + ₀^ n( x)^ n-1 x e^ -x d x=0+n ( ( x)^ n-1 x e^ -x -1 )₀^ +n ₀^ [( x)^ n-1 (- x)+( x)(n-1) x( x)^ n-2 x ] e^ -x d x=n ₀^ (-( x)^n+(n-1) (1- ^2 x )( x)^ n-2 ) e^ -x d x= n(n-1) n^2+1 I_ n-2 101 I ₁₀ I ₈ =101 10 9 10^2+1 =90 .

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