Question

${\int }_0^2\left[x^2\right]$ is equal to

• A. $1$
• B. $5-\sqrt{2}-\sqrt{3}$
• C. $3-\sqrt{2}$
• D. $\frac{8}{3}$

Answer 1

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

$\underset{0}{\overset{1}{\int }}0dx+\underset{1}{\overset{\sqrt{2}}{\int }}1dx+\underset{\sqrt{2}}{\overset{\sqrt{3}}{\int }}2dx+\underset{\sqrt{3}}{\overset{2}{\int }}3dx=(\sqrt{2}-1)+2(\sqrt{3}-\sqrt{2})+3(2-\sqrt{3})=5-\sqrt{3}-\sqrt{2}.$