Value of $\int\limits_0^n[x] d x$ (where n ∈ N) is
Answer & explanation
Correct answer: option 2
$\int\limits_0^n[x] d x=\sum\limits_{i=1}^n \int\limits_{i-1}^i[x] d x$
$\sum\limits_{i=1}^n(i-1) d x=\frac{n(n-1)}{2}$
Hence (2) is the correct answer.
Value of $\int\limits_0^n[x] d x$ (where n ∈ N) is
Correct answer: option 2
$\int\limits_0^n[x] d x=\sum\limits_{i=1}^n \int\limits_{i-1}^i[x] d x$
$\sum\limits_{i=1}^n(i-1) d x=\frac{n(n-1)}{2}$
Hence (2) is the correct answer.