Question

If $\left[x\right]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\underset{0}{\overset{2}{\int }}{x}^2\left[x\right]dx$ equals

• A. $\frac{5}{3}$
• B. $\frac{7}{3}$
• C. $\frac{8}{3}$
• D. $\frac{4}{3}$

Answer 1

The correct option is B $\frac{7}{3}$

$\underset{0}{\overset{2}{\int }}{x}^2\left[x\right]dx=0+\underset{1}{\overset{2}{\int }}{x}^2.1.dx$

$={\left[\frac{x^3}{3}\right]}_1^2$

$=\frac{7}{3}$