Question

The area bounded by $y=x^2,y=[x+1],x\le 1$ and the $y-$ axis is
$\left(\right[\cdot \left]\text{denotes the greatest integer function.}\right)$

• A. $\frac{1}{3}\text{sq. units}$
• B. $\frac{2}{3}\text{sq. units}$
• C. $1\text{sq. units}$
• D. $\frac{7}{3}\text{sq. units}$

Answer 1

The correct option is B $\frac{2}{3}\text{sq. units}$

$y=x^2$ and $y=\left[x\right]+1$
$A={\int }_0^1(1-x^2)dx=\frac{2}{3}\text{sq. units}$