Question

The area under the curve 2{y} = [x] + 1, $0\le y<1$ (where {.} and [.] are the fractional part and greatest integer functions respectively) and the x axis is (in square units)

• A. $\frac{1}{2}$
• B. 1
• C. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{1}{2}$

$2\left\{y\right\}=\left[x\right]+1$
$0\le y<1$
$\begin{array}{cc}\{y=y\}and& 0\le \left[x\right]+1<2\\ & -1\le \left[x\right]<1\\ When-1<x<0& y=0\\ 0\le x<1& y=\frac{1}{2}\\ Area=\frac{1}{2}& \end{array}$