A) \[2-\sqrt{2}\]
B) \[2+\sqrt{2}\]
C) \[\sqrt{2}-1\]
D) \[-\sqrt{2}-\sqrt{3}+5\]
Correct Answer: D
Solution :
\[\int_{0}^{1}{[{{x}^{2}}]}dx+\int_{1}^{\sqrt{2}}{[{{x}^{2}}]}\,dx+\int_{\sqrt{2}}^{\sqrt{3}}{[{{x}^{2}}]}\,dx\] \[+\int_{\sqrt{3}}^{2}{[{{x}^{2}}]\,}dx\] \[\int_{0}^{1}{[{{x}^{2}}]}\,dx+\int_{1}^{\sqrt{2}}{[{{x}^{2}}]}\,dx+\int_{\sqrt{2}}^{\sqrt{3}}{[{{x}^{2}}]}\,dx\] \[=0+1(\sqrt{2}-1)+2(\sqrt{3}-\sqrt{2})+3(2-\sqrt{3})\] \[=5-\sqrt{3}-\sqrt{2}\]
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