If `[dot]a n d\ {dot}` denote respectively the greatest integer and fractional part functional respectively, evaluate the following integral: `int_0^(15)[x]dx`

Explanation

A= `int_0^15 [x] dx`

`[x]`

`xle [x] lt x=1`

`1le [x] lt 2 rightarrow 1`

`2le [x] lt 3 rightarrow 2`

`3 le [x] lt 4 rightarrow 3`

`A = int_0^1 [x]dx + int_1^2 [x]dx + int_2^3 [x]dx + ldots + int_14^15 [x] dx`

`=0+1+2+3+ ldots + 13 + 14`

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