Let I_ n = ₀¹( x)^ n d x , where n is a non-negative integer. Then I₂₀₀₁-2011 I₂₀₁₀ is equal to-

Step-by-step solution

I_ n = ₁^ e 1 . ( ₁ x )^ n d x array l I_ n = .( x)^ n x |₁ ^ e - ₁^ e n( x)^ n-1 x x d x I_ n =e-0-n I_ n-1 I_ n +n I_ n-1 =e I_ 2001+2011 I₂₀₁₀=e ₁₀₀+100 I ₉₉=e array