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The area enclosed between the curve\[y={{\log }_{e}}(x+e)\]and the coordinate axes is     AIEEE  Solved  Paper-2005

A) 4             

B)        3             

C)        2             

D)        1

Correct Answer: D

Solution :

Required area, \[A=\int_{1-e}^{0}{{{\log }_{e}}}(x+e)dx\] Put \[x+e=t\Rightarrow dx=dt\] \[\therefore \]\[A=\int_{1}^{e}{{{\log }_{e}}}t\,dt=(t\,{{\log }_{e}}t-t)_{1}^{e}\] \[=(e-e-0+1)=1\]