_0^1.5 [x] dx, where [x] denotes the greatest integer function ≤ x, is equal to : Option 1: 1/4 Option 2: 1/2 Option 3: 1 Option 4: 0

Answer: 1/2. Solution: Split the integral: _0^1.5 [x] dx = _0^1 0 dx + _1^1.5 1 dx = 0 + 0.5 = 1/2.

Calculus

Integrals

Easy

common

$\int_{0}^{1.5} [x] dx$ , where $[x]$ denotes the greatest integer function $\leq x$ , is equal to :

$\frac{1}{4}$

$\frac{1}{2}$

$1$

$0$

✅ Correct Option: 2

Split the integral: $\int_0^{1.5} [x]\,dx = \int_0^1 0\,dx + \int_1^{1.5} 1\,dx = 0 + 0.5 = \frac{1}{2}$ .

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∫01.5[x]dx\int_{0}^{1.5} [x] dx∫01.5​[x]dx, where [x][x][x] denotes the greatest integer function ≤x\leq x≤x, is equal to :

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$\int_{0}^{1.5} [x] dx$ , where $[x]$ denotes the greatest integer function $\leq x$ , is equal to :