Let `[x]` denote the greatest integer less than or equal to `x`. Then, `int_(0)^(1.5)[x]dx=?`A. `(1)/(2)`B. `(3)/(2)`C. `2`D. `3`

Let `[x]` denote the greatest integer less than or equal to `x`. Then,

1.	Let `[x]` denote the greatest integer less than or equal to `x`. Then, `int_(0)^(1.5)[x]dx=?`A. `(1)/(2)`B. `(3)/(2)`C. `2`D. `3`
Answer» `{0 le x lt 1implies[x]=0}` and `{1 le x lt 1.5}implies[x]=1` `:. I=int_(0)^(1)[x]dx+int_(1)^(1.5)[x]dx=int_(0)^(1)0dx+int_(0)^(1.5)1*dx` `=0+[x]_(1)^(1.5)=(1.5-1)=0.5=(1)/(2)`.

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