Area Ques 55
Question
- 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)
Show Answer
Answer:
Correct Answer: 55.$(\frac{4-\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2}) \text { sq units }$
Solution:
Formula:
- 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} _{1/2} \\ & =(\frac{4-\sqrt{2}}{\log 2}-\frac{5}{2} \log 2+\frac{3}{2}) \text { sq units } \end{aligned} $
BETA
