Answer:
Let \[l=\int_{1}^{2}{{{\log }_{e}}[x]dx,}\] \[=\int_{1}^{2}{{{\log }_{e}}1dx,}\] \[[\because \,\,[x]=1,\,\,x\in [1,\,\,2]]\] = 0 \[[\because \,\,{{\log }_{e}}1=0]\]
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