Question

The area bounded by $y=x^2,y=[x+1],x\le 1$ and the y-axis is, where $[.]$ is greatest integer function

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

Answer 1

The correct option is B $\frac{2}{3}$

Since, $0\le x\le 1$

Therefore, $y=[x+1]=1$

Hence, required area = ${\int }_0^1\sqrt{y}dy$

$=\frac{2}{3}[y^{3/2}{]}_0^1$

$=\frac{2}{3}$ sq. units