A) \[0\]
B) \[\frac{3}{2}\]
C) \[\frac{3}{4}\]
D) \[\frac{5}{4}\]
Correct Answer: C
Solution :
\[\int\limits_{0}^{1}{x[{{x}^{2}}]dx}+\int\limits_{1}^{\sqrt{2}}{x[{{x}^{2}}]dx}+\int\limits_{\sqrt{2}}^{1.5}{x}[{{x}^{2}}]dx\] \[\int\limits_{0}^{1}{x.0dx}+\int\limits_{1}^{\sqrt{2}}{xdx}+\int\limits_{\sqrt{2}}^{1.5}{2xdx}\] \[0+\left[ \frac{{{x}^{2}}}{2} \right]_{1}^{\sqrt{2}}+\left[ {{x}^{2}} \right]_{\sqrt{2}}^{1.5}\] \[\frac{1}{2}(2-1)+(2.25-2)\] \[\frac{1}{2}+.25\]
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