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If $n \in N$ , the value of $\int_{0}^{n} [x] d x$ (where $(x)$ is the greatest integer function) is

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n(n+1)2

n(n-1)2

n (n – 1)

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detailed solution

Correct option is B

∫0n [x]dx=∑i=1n ∫i−1i [x]dx=∑i=1n ∫i−1i (i−1)dx=∑i=1n (i−1)=n(n−1)2.

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If n ∈ N , the value of ∫0n [x]dx (where (x) is the greatest integer function) is

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If $n \in N$ , the value of $\int_{0}^{n} [x] d x$ (where $(x)$ is the greatest integer function) is