Area Question 44
Question 44
- Sketch the curves and identify the region bounded by $x=1 / 2, x=2, y=\log x$ and $y=2^{x}$. Find the area of this region.
(1991, 4M)
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Solution:
- The required area is the shaded portion in following figure
$\therefore$ The required area
$$ \begin{aligned} & =\int_{1 / 2}^{2}\left(2^{x}-\log x\right) d x=\frac{2^{x}}{\log 2}-(x \log x-x)^{2} \ & =\frac{4-\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2} \text { sq units } \end{aligned} $$
