Question

The area (in sq. units) of the region bounded by the curves $y=2^x$ and $y=|x+1|$, in the first quadrant is:

• A. $\frac{3}{2}-\frac{1}{{\log }_{e}2}$
• B. $\frac{1}{2}$
• C. ${\log }_{e}2+\frac{3}{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $\frac{3}{2}-\frac{1}{{\log }_{e}2}$

Required Area
${\int }_0^1((x+1)-2^x)dx={(\frac{x^2}{2}+x-\frac{2^x}{\ln 2})}_0^1=(\frac{1}{2}+1-\frac{2^{}}{\ln 2})-(0+0-\frac{1}{\ln 2})=\frac{3}{2}-\frac{1}{\ln 2}$