question_answer

Area enclosed by the graph of \[y={{\log }_{e}}(x+1),\]y-axis, and the line \[y=1\] is

A) \[e-2\]           

B)        \[e-1\]                

C) \[e\]                   

D)        \[2e\]

Correct Answer: A

Solution :

     [a] Required area, \[A=\int\limits_{0}^{1}{({{e}^{y}}-1)\,\,dy=\left[ {{e}^{y}}-y \right]_{0}^{1}=e-2}\]