Question

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int\limits^{{2}}_{{0}}x^2 [x] dx$

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

Answer 1

Answer: (B)

$\frac{7}{3}$

Answer 2

$\int\limits^{{2}}_{{0}}x^2 [x] \cdot dx=\int\limits^{{1}}_{{0}}x^2\times 0dx+\int\limits^{{2}}_{{1}}x^2 \times 1dx=(x^3/3)^2_1=7/3$