A) \[2-\sqrt{2}\]
B) \[2+\sqrt{2}\]
C) \[\sqrt{2}-1\]
D) \[-\sqrt{2}-\sqrt{3}+5\]
Correct Answer: D
Solution :
\[\int_{0}^{2}{[{{x}^{2}}]dx}\] \[=\int_{0}^{1}{[{{x}^{2}}]dx+\int_{1}^{\sqrt{2}}{[{{x}^{2}}]dx+\int_{\sqrt{2}}^{\sqrt{3}}{[{{x}^{2}}]dx+\int_{\sqrt{3}}^{2}{[{{x}^{2}}]dx}}}}\] \[=\int_{0}^{1}{0dx+\int_{0}^{\sqrt{2}}{1dx}}+\int_{\sqrt{2}}^{\sqrt{3}}{2dx}+\int_{\sqrt{3}}^{2}{3dx}\] \[=[x]_{1}^{\sqrt{2}}+[2x]_{\sqrt{2}}^{\sqrt{3}}+[3x]_{\sqrt{3}}^{2}\] \[=\sqrt{2}-1+2\sqrt{3}-2\sqrt{2}+6-3\sqrt{3}\] \[=5-\sqrt{3}-\sqrt{2}\]
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