question_answer

The area (in sq. units) of the region bounded by the curves \[y={{2}^{x}}\]and \[y=\left| x+1 \right|,\] in the first quadrant is : [JEE Main 10-4-2019 Afternoon]

A) \[\frac{3}{2}-\frac{1}{{{\log }_{e}}2}\]     

B) \[\frac{1}{2}\]

C) \[{{\log }_{e}}2+\frac{3}{2}\]                    

D) \[\frac{3}{2}\]

Correct Answer: A

Solution :

Required Area\[\int\limits_{0}^{1}{\left( \left( x+1 \right)-{{2}^{x}} \right)}dx\]                                   \[=\left( \frac{1}{2}+1-\frac{2}{\ln 2} \right)-\left( 0+0-\frac{1}{\ln 2} \right)\]             \[=\frac{3}{2}-\frac{1}{\ln 2}\]