CUET Preparation Today
The expression $\frac{\int\limits_0^n[x]dx}{\int\limits_0^n\{x\}dx}$, where [x] and {x} are integral and fractional part of x and n ∈ N, is equal to: |
n + 1 1/n n n – 1 |
n – 1 |
$I=\frac{\int\limits_0^n[x]dx}{\int\limits_0^n\{x\}dx}=\frac{0+1+2+....+(n-1)}{\frac{1}{2}+\frac{1}{2}+....+\,n\,times}=n-1$
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