Question

Evaluate ${\int }_0^2\left[x^2\right]dx$

• 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 A $5-\sqrt{2}-\sqrt{3}$

${\int }_0^2\left[x^2\right]dx={\int }_0^{1}0\cdot dx+{\int }_1^{\sqrt{2}}dx+{\int }_{\sqrt{2}}^{\sqrt{2}}2\cdot dx+3{\int }_{\sqrt{3}}^{2}dx$
$=5-\sqrt{2}-\sqrt{3}$