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Integral of x^2 [x] from 0 to n, [x] the greatest integer function

The same question, asked 2 times: 16 May 2023 S2*, 20 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S2

    126
    If [x][x] denotes the greatest integer function, then ∫05x2[x] dx=\int_0^5 x^2[x]\,dx =

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  2. Question 2

    20 Apr 2026 S1

    81
    If [x][x] denotes the greatest integer less than or equal to xx, then the value of the integral ∫02x2[x] dx\int_0^2 x^2[x]\,dx is equal to

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