• # question_answer Let $[\cdot ]$denotes the greatest integer function, then $\int_{1}^{2}{[3\,x]}$ is equal to A)  4                                 B)  5 C)  6                                 D)  7

$\int_{1}^{2}{[3x]\,dx=}\,\int_{1}^{1/3}{[3x]\,dx+}\,\int_{4/3}^{5/3}{[3x]\,dx}$ $+\,\int_{5/3}^{2}{[3x]\,dx}$ $=3\,\left( \frac{4}{3}-1 \right)+4\,\left( \frac{5}{3}-\frac{4}{3} \right)+5\,\left( 2-\frac{5}{3} \right)=4$