A) \[{{e}^{{{x}^{2}}}}\]
B) \[\frac{1}{2}{{e}^{{{x}^{2}}}}\]
C) \[2{{e}^{{{x}^{2}}}}\]
D) \[\frac{{{e}^{{{x}^{2}}}}-{{x}^{2}}}{2}\]
Correct Answer: B
Solution :
\[\int_{{}}^{{}}{{{e}^{{{x}^{2}}}}.x\,dx}=\frac{1}{2}\int_{{}}^{{}}{(2x){{e}^{{{x}^{2}}}}dx}\] \[=\frac{1}{2}\int_{{}}^{{}}{{{e}^{t}}dt}=\frac{1}{2}{{e}^{t}}=\frac{1}{2}{{e}^{{{x}^{2}}}}\], (Put \[{{x}^{2}}=t\Rightarrow dt=2x\,dx)\].
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