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 :
Correct Option: 4,
Solution:
Area $=\int_{0}^{1}\left((x+1)-2^{x}\right) d x$ $\left(\because\right.$ Area $\left.=\int y d x\right)$
$=\left[\frac{x^{2}}{2}+x-\frac{2^{x}}{\ln 2}\right]_{0}^{1}=\left(\frac{1}{2}+1-\frac{2}{\ln 2}\right)-\left(\frac{-1}{\ln 2}\right)=\frac{3}{2}-\frac{1}{\ln 2}$
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