question_answer

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

A)  3                                            

B)         4                            

C)         1                                            

D)         2

Correct Answer: C

Solution :

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