Greatest Integral

Calculus Level 4

\[\large \Upsilon = \displaystyle\int_0^n [ x ] \text{dx} \]

Choose the correct option:

A) If n is an integer then \(\Upsilon = \dfrac{n(n + 1)}{2}\)

B) If n = x then \(\Upsilon = x[x] - \dfrac{[x]}{2}( [x] +1)\)

C) If n = x then \(\Upsilon = x[x] + \dfrac{[x]}{2}( [x] +1)\)

D)If n is an integer then \(\Upsilon = \dfrac{(n - 1)(n + 1)}{2}\)

Details:

  • \( n > 0 \)
  • [ . ] represents Greatest Integer function
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