Question

The value of integral $\underset{0}{\overset{3}{\int }}\left[x\right]dx=$

Answer 1

$I=\underset{0}{\overset{3}{\int }}\left[x\right]dx=\underset{0}{\overset{1}{\int }}\left[x\right]dx+\underset{1}{\overset{2}{\int }}\left[x\right]dx+\underset{2}{\overset{3}{\int }}\left[x\right]dx$
$=\underset{0}{\overset{1}{\int }}0dx+\underset{1}{\overset{2}{\int }}1dx+\underset{2}{\overset{3}{\int }}2dx$
$=[x{]}_1^2+2[x{]}_2^3=1+2=3$