question_answer

    Area bounded by the curve\[y={{\log }_{e}}x,x=0,y\le 0\]and\[x-\]axis is

A)  1 sq unit             

B)  1/2 sq unit

C)  2 sq unit             

D)  none of these

Correct Answer: A

Solution :

                Given curve\[y=lo{{g}_{e}}x,\text{ }x=0,\text{ }y\le 0\]and\[x-\]axis \[\therefore \]Bounded region is \[\therefore \]Required area is \[\left| \int_{0}^{1}{{{\log }_{e}}x\,dx} \right|\]\[=[|x{{\log }_{e}}x-x|]_{0}^{1}=1\,sq\,unit\]