Question

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

• A. $5-\sqrt{2}+\sqrt{3}$
• B. $5-\sqrt{2}-\sqrt{3}$
• C. $-5-\sqrt{2}-\sqrt{3}$
• D. $5+\sqrt{2}-\sqrt{3}$

Answer 1

The correct option is B $5-\sqrt{2}-\sqrt{3}$

$\underset{0}{\overset{2}{\int }}\left[x^2\right]dx=\underset{0}{\overset{1}{\int }}\left[x^2\right]dx+\underset{1}{\overset{\sqrt{2}}{\int }}\left[x^2\right]dx+\underset{\sqrt{2}}{\overset{\sqrt{3}}{\int }}\left[x^2\right]dx+\underset{\sqrt{3}}{\overset{2}{\int }}\left[x^2\right]dx$
$=\underset{0}{\overset{1}{\int }}0dx+\underset{1}{\overset{\sqrt{2}}{\int }}1dx+\underset{\sqrt{2}}{\overset{\sqrt{3}}{\int }}2dx+\underset{\sqrt{3}}{\overset{2}{\int }}3dx$
$=0+(\sqrt{2}-1)+2(\sqrt{3}-\sqrt{2})+3(2-\sqrt{3})$
$=5-\sqrt{2}-\sqrt{3}$