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Evaluate (int(0)^(n)[x]dx)/(int(0)^(n){x...

Evaluate `(int_(0)^(n)[x]dx)/(int_(0)^(n){x}dx)` (where `[x]` and `{x}` are integral and fractional parts of `x` respectively and `n epsilon N`).

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`I=(int_(0)^(n)[x]dx)/(int_(0)^(n){x}dx)`
`=int_(0)^(n)(x-{x}dx)/(int_(0)^(n){x}dx)`
`=(int_(0)^(n)x dx)/(int_(0)^(n){x]dx)-1`
`=((x^(2))/2|_(0)^(n))/(n int_(0)^(1){x}dx)-1`
`=((n^(2))/2)/(n int_(0)^(1)x dx)-1`
`=((n^(2))/2)/(n 1/2)-1=n-1`
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