A) \[\frac{1}{2}[{{x}^{2}}{{\{F(x)\}}^{2}}-\int{{{\{F(x)\}}^{2}}dx]}\]
B) \[\frac{1}{2}[{{x}^{2}}F{{(x)}^{2}}-\int{F{{(x)}^{2}}d{{(x)}^{2}}]}\]
C) \[\frac{1}{2}[{{x}^{2}}F(x)-\frac{1}{2}\int{{{\{F(x)\}}^{2}}dx]}\]
D) None of the above
Correct Answer: B
Solution :
We have,\[\int{f(x)=dx}=F(x)\] \[\therefore \]\[\int{{{x}^{2}}f({{x}^{2}})dx=\frac{1}{2}\int{{{x}^{2}}}f{{(x)}^{2}}d{{(x)}^{2}}}\] \[=\frac{1}{2}[{{x}^{2}}F({{x}^{2}})-\int{F({{x}^{2}})d({{x}^{2}})]}\]
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