A) \[\log \left( \frac{e}{2} \right)\]
B) \[\log \left( \frac{2}{e} \right)\]
C) \[\log \left( \frac{e}{4} \right)\]
D) \[\log \left( \frac{4}{e} \right)\]
Correct Answer: D
Solution :
Let \[I=\int_{1}^{2}{1.\log x\,dx}\] \[=[x\log x-\int_{{}}^{{}}{1\,dx}]_{1}^{2}\] \[=[x\log x-x]_{1}^{2}\] \[=2\log 2-2-(0-1)\] \[=2\log 2-1={{\log }_{e}}{{2}^{2}}-{{\log }_{e}}e\] \[=\log \left( \frac{4}{e} \right)\]
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