question_answer

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

A)            3    

B)            4

C)            1    

D)            2

Correct Answer: C

Solution :

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