A) \[{{(e-1)}^{2}}\]
B) \[{{e}^{2}}-e+1\]
C) \[{{e}^{2}}-e+1-2lo{{g}_{e}}2\]
D) \[{{e}^{2}}+e-2lo{{g}_{e}}2\]
Correct Answer: C
Solution :
Required area, \[A=\int_{1}^{2}{({{e}^{x}}-{{\log }_{e}}x)}\,dx\] \[=[{{e}^{x}}]_{1}^{2}-[x{{\log }_{e}}x-\int{1\,dx}]_{1}^{2}\] \[={{e}^{2}}-e-[x{{\log }_{e}}x-x]_{1}^{2}\] \[={{e}^{2}}-e-[2{{\log }_{e}}2-2(0-1)]\] \[={{e}^{2}}-e-2{{\log }_{e}}2+1\]You need to login to perform this action.
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