Let `I_(n) = int_(0)^(1) (logx)^(n)dx`, where n is a non-negative integer. Then `I_(2001) - 2011 I_(2010)` is equal to -A. `I_(1000) + 999 I_(998)`B. `I_(890) + 890 I_(889)`C. `I_(100) + 100 I_(99)`D. `I_(53) + 54 I_(52)`

Let `I_(n) = int_(0)^(1) (logx)^(n)dx`, where n is a non-negative inte

1.	Let `I_(n) = int_(0)^(1) (logx)^(n)dx`, where n is a non-negative integer. Then `I_(2001) - 2011 I_(2010)` is equal to -A. `I_(1000) + 999 I_(998)`B. `I_(890) + 890 I_(889)`C. `I_(100) + 100 I_(99)`D. `I_(53) + 54 I_(52)`
Answer» Correct Answer - C `I_(n)=overset(e)underset(1)intunderset(II)(1).underset(I)((logx)^(n))dx` ` I_(n) (logx)^(n)x\|_(1)^(e)-overset(e)underset(1)int(n(logx)^(n-1))/(x).xdx` `I_(n) = e - 0 - nI_(n-1)` `I_(n) + nI_(n-1) = e` `I_(2001+2011)I_(2010) = e` `I_(100) + 100I_(99) = e`

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Let `I_(n) = int_(0)^(1) (logx)^(n)dx`, where n is a non-negative integer. Then `I_(2001) - 2011 I_(2010)` is equal to -A. `I_(1000) + 999 I_(998)`B. `I_(890) + 890 I_(889)`C. `I_(100) + 100 I_(99)`D. `I_(53) + 54 I_(52)`

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