Question

${\int }_{0.2}^{3.5}\left[x\right]dx$ is equal to

• A. 3
• B. 3.5
• C. 4.5
• D. 4

Answer 1

Answer: (C)

4.5

${\int }_{0.2}^{3.5}\left[x\right]dx={\int }_{0.2}^1\left[x\right]dx+{\int }_1^2\left[x\right]dx+{\int }_2^3\left[x\right]+{\int }_3^{3.5}\left[x\right]dx$

$={\int }_{0.2}^1\left(0\right)dx+{\int }_1^2\left(1\right)dx+{\int }_2^3\left(2\right)dx+{\int }_3^{3.5}\left(3\right)dx$

$=0+{\left|x\right|}_1^2+2{\left|x\right|}_2^3+3{\left|x\right|}_3^{3.5}$

$=(2-1)+2(3-2)+3(3.5-3)$

$=1+2+3\left(0.5\right)$

$=3+1.5$

$=4.5$