question_answer

The area of the region bounded by the curve \[y=lo{{g}_{e}}(x+e)\]and axes is

A)  1               

B)  2

C)  3               

D)  4

Correct Answer: A

Solution :

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